Self-immolation is the act of sacrificing oneself by setting oneself on fire and burning to death. It is typically used for political or religious reasons, often as a form of non-violent protest or in acts of martyrdom. It has a centuries-long recognition as the most extreme form of protest possible by humankind.
Etymology
The English word immolation
originally meant (1534) "killing a sacrificial victim; sacrifice" and
came to figuratively mean (1690) "destruction, especially by fire". Its
etymology was from Latinimmolare "to sprinkle with sacrificial meal (mola salsa); to sacrifice" in ancient Roman religion.
Self-immolators
frequently use accelerants before igniting themselves on fire. This,
combined with the self-immolators' refusal to protect themselves, can
produce hotter flames and deeper, more extensive burns. Most of the time, it leads to amputation of extremities.
Self-immolation has been described as excruciatingly painful.
Later the burns become severe, nerves are burnt and the self-immolator
loses sensation at the burnt areas. Some self-immolators can die during
the act from inhalation of toxic combustion products, hot air and flames. A while later, their body releases adrenaline.
The body has an inflammatory response to burnt skin which happens
after 25% is burnt in adults. This response leads to blood and body
fluid loss. If the self-immolator is not taken to a burn centre in less
than four hours, they are more likely to die from shock. If no more than
80% of their body area is burnt and the self-immolator is younger than
40 years old, there is a survival chance of 50%. If the self-immolator
has over 80% burns, the survival rate drops to 20%.
Self-immolation is tolerated by some elements of Mahayana Buddhism and Hinduism, and it has been practiced for many centuries, especially in India, for various reasons, including jauhar, political protest, devotion, and renouncement. An example from mythology includes the practice of Sati when the Hindu goddess Parvati's incarnation of the same name (see also Daksayani)
legendarily set herself on fire after her father insulted her in Daksha
Yajna for having married Shiva, the ascetic god. Shiva, Parvati and
their army of ghosts attacked Daksha's Yajna and destroyed the sacrifice
and Shiva beheaded Daksha and killed Daksha. Later, Daksha was revived
by him and Daksha Yajna was completed when Daksha apologized. Certain
warrior cultures, such as those of the Charans and Rajputs, also practiced self-immolation.
Zarmanochegas was a monk of the Sramana tradition (possibly, but not necessarily a Buddhist) who, according to ancient historians such as Strabo and Dio Cassius, met Nicholas of Damascus in Antioch around 22 BC and burnt himself to death in Athens shortly thereafter.
The monk Fayu 法羽 (d. 396) carried out the earliest recorded Chinese self-immolation. He first informed the "illegitimate" prince Yao Xu 姚緒—brother of Yao Chang who founded the non-Chinese Qiang state Later Qin
(384–417)—that he intended to burn himself alive. Yao tried to dissuade
Fayu, but he publicly swallowed incense chips, wrapped his body in
oiled cloth, and chanted while setting fire to himself. The religious
and lay witnesses were described as being "full of grief and
admiration".
Following Fayu's example, many Buddhist monks and nuns have used
self-immolation for political purposes. Based upon analysis of Chinese
historical records from the 4th to the 20th centuries, some monks did
offer their bodies in periods of relative prosperity and peace, but
there is a "marked coincidence" between acts of self-immolation and
times of crisis, especially when secular powers were hostile towards Buddhism. For example, Daoxuan's (c. 667) Xu Gaoseng Zhuan (續高僧傳, or Continued Biographies of Eminent Monks) records five monastics who self-immolated on the Zhongnan Mountains in response to the 574–577 persecution of Buddhism by Emperor Wu of Northern Zhou (known as the "Second Disaster of Wu").
A Hindu widow burning herself with the corpse of her husband (sati), 1657
For many monks and laypeople in Chinese history, self-immolation was a
form of Buddhist practice that modeled and expressed a particular path
that led towards Buddhahood.
Historian Jimmy Yu has stated that self-immolation cannot be
interpreted based on Buddhist doctrine and beliefs alone but the
practice must be understood in the larger context of the Chinese
religious landscape. He examines many primary sources from the 16th and
17th century and demonstrates that bodily practices of self-harm,
including self-immolation, was ritually performed not only by Buddhists
but also by Daoists
and literati officials who either exposed their naked body to the sun
in a prolonged period of time as a form of self-sacrifice or burned
themselves as a method of procuring rain. In other words, self-immolation was a sanctioned part of Chinese culture
that was public, scripted, and intelligible both to the person doing
the act and to those who viewed and interpreted it, regardless of their
various religion affiliations.
During the Great Schism of the Russian Church, entire villages of Old Believers burned themselves to death in an act known as "fire baptism" (self-burners: soshigateli). Scattered instances of self-immolation have also been recorded by the Jesuit priests of France in the early 17th century. However, their practice of this was not intended to be fatal: they would burn certain parts of their bodies (limbs such as the forearm or the thigh) to symbolise the pain Jesus endured while upon the cross.
A 1973 study by a prison doctor suggested that people who choose
self-immolation as a form of suicide are more likely to be in a
"disturbed state of consciousness", such as epilepsy.
Political protest
As a form of political protest, the 14th Dalai Lama explained in 2013 and 2015 the act of self-immolation:
I think the self-burning itself on
practice of non-violence. These people, you see, they [could instead]
easily use bomb explosive, more casualty people. But they didn't do
that. Only sacrifice their own life. So this also is part of practice of
non-violence.
Self-immolations are often public and political statements that are
often reported by the news media. They can be seen by others as a type
of altruistic suicide for a collective cause, and are not intended to inflict physical harm on others or cause material damage. They attract attention to a specific cause and those who undergo the act may be seen as martyrs.
Self-immolation does not guarantee death for the burned;
self-immolation survivors suffer from severe disfigurements from
resulting burns.
The Buddhist crisis in South Vietnam saw the persecution of the country's majority religion under the administration of Catholic president Ngô Đình Diệm. Several Buddhist monks, including the most famous case of Thích Quảng Đức, immolated themselves in protest.
The example set by self-immolators in the mid 20th century did
spark numerous similar acts between 1963 and 1971, most of which
occurred in Asia and the United States in conjunction with protests
opposing the Vietnam War. Researchers counted almost 100 self-immolations covered by The New York Times and The Times.
Soviet Bloc
In 1968 the practice spread to the Soviet bloc with the self-immolation of Polish accountant and Armia Krajowa veteran Ryszard Siwiec, as well as those of two Czech students, Jan Palach and Jan Zajíc, and of toolmaker Evžen Plocek, in protest against the Warsaw Pact invasion of Czechoslovakia. As a protest against Soviet rule in Lithuania, 19-year-old Romas Kalanta set himself on fire in Kaunas in 1972. In 1978 Ukrainian dissident and former political prisoner Oleksa Hirnyk
burnt himself near the tomb of the Ukrainian poet Taras Shevchenko
protesting against the russification of Ukraine under Soviet rule. On 2
March 1989, Liviu Cornel Babeș
set himself on fire on the Bradu ski slope at Poiana Brașov as a sign
of protest against the communist regime. He left the message: „Stop Mörder! Brașov = Auschwitz". He was taken to the Brașov county hospital, where he died two hours later.
Russian Federation
In 2020, the practice resumed when Russian journalist Irina Slavina burned herself in Nizhny Novgorod after her last post on Facebook, in which she wrote: "I ask you to blame the Russian Federation for my death".
Also, cases of self-immolation as a form of political protest were
recorded in Moscow, St. Petersburg, Ufa, Izhevsk, Kemerovo and other
cities of the Russian Federation. Most of the cases were fatal.
India
The
practice continues, notably in India: as many as 1,451 and 1,584
self-immolations were reported there in 2000 and 2001, respectively. A particularly high wave of self-immolation in India was recorded in 1990 protesting the Reservation in India. Tamil Nadu has the highest number of self-immolations in India to date.
Iran
In Iran, most self-immolations have been performed by citizens protesting the tempestuous changes brought upon after the Iranian Revolution.
Many of these instances have gone largely unreported by regime
authority, but have been discussed and documented by established
witnesses. Provinces that were involved more intensively in postwar
problems feature higher rates of self-immolation.
These undocumented demonstrations of protest are deliberated upon
worldwide, by professionals such as Iranian historians who appear on
international broadcasts such as Voice of America, and use the immolations as propaganda to direct criticism towards the Censorship in Iran. One specifically well documented self-immolation transpired in 1993, 14 years after the revolution, and was performed by Homa Darabi, a self-proclaimed political activist affiliated with the Nation Party of Iran. Darabi is known for her political self-immolation in protest to the compulsory hijab.
Self-immolation protests continue to take place against the regime to
this day. Most recently accounted for is the September 2019 death of Sahar Khodayari, protesting a possible sentence of six months in prison for having tried to enter a public stadium to watch a football
game, against the national ban against women at such events. One month
after her death, Iranian women were allowed to attend a football match
in Iran for the first time in 40 years.
In 2009, the monk Tapey at Kirti Monastery in Amdo self-immolated in protest of the Chinese government's restrictions placed against an important ceremony.
A wave of self-immolations began in 2011, after another monk, Phuntsok, also from Kirti Monastery self-immolated.
The wave continued until 2019 and resumed again in 2022. As of April
2022, there were 161 confirmed cases in Tibet and 10 others made in
solidarity outside of Tibet. With the self-immolations by Tibetans,
most of these protests (some 80%) end in death, while eyewitness report
state many of the protestors have been shot and beaten while burning,
and then arrested by Chinese authorities and disappeared.
The 14th Dalai Lama has spoken with respect and compassion for those who engage in self-immolation, and blamed the self-immolations on "cultural genocide" by the Chinese. The Chinese government claims that he and the exiled Tibetan government are inciting these acts.
In 2013, the Dalai Lama questioned the effectiveness of self-immolation
as a demonstration tactic. He has also expressed that the Tibetans are
acting of their own free will and stated that he cannot influence them
to stop carrying out immolation as a form of protest.
On 3 December 2020, a Taiwanese man self-immolated to protest closure of CTi News.
Australia
On 1
January 2022, an Australian man self-immolated to protest the COVID-19
vaccine mandates and vaccine IDs. He was later taken to the hospital.
United States
On 14 April 2018, David Buckel self immolated in Prospect Park
in Brooklyn. Shortly before lighting himself on fire he sent an email
to several news outlets which included the statement "Most humans on the
planet now breathe air made unhealthy by fossil fuels, and many die
early deaths as a result—my early death by fossil fuel reflects what we
are doing to ourselves."
Wynn Bruce, a climate activist from Boulder, Colorado self-immolated on the steps of the Supreme Court of the United States on Earth Day,
22 April 2022. On 28 March 2022, he made a Facebook post stating “This
is not humor. It is all about breathing” followed by “Clean air
matters.”
The universe of the Game of Life is an infinite, two-dimensional orthogonal grid of squarecells, each of which is in one of two possible states, live or dead (or populated and unpopulated, respectively). Every cell interacts with its eight neighbours,
which are the cells that are horizontally, vertically, or diagonally
adjacent. At each step in time, the following transitions occur:
Any live cell with fewer than two live neighbours dies, as if by underpopulation.
Any live cell with two or three live neighbours lives on to the next generation.
Any live cell with more than three live neighbours dies, as if by overpopulation.
Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
These rules, which compare the behavior of the automaton to real life, can be condensed into the following:
Any live cell with two or three live neighbours survives.
Any dead cell with three live neighbours becomes a live cell.
All other live cells die in the next generation. Similarly, all other dead cells stay dead.
The initial pattern constitutes the seed of the system. The
first generation is created by applying the above rules simultaneously
to every cell in the seed, live or dead; births and deaths occur
simultaneously, and the discrete moment at which this happens is
sometimes called a tick. Each generation is a pure function of the preceding one. The rules continue to be applied repeatedly to create further generations.
Origins
Stanislaw Ulam, while working at the Los Alamos National Laboratory in the 1940s, studied the growth of crystals, using a simple lattice network as his model. At the same time, John von Neumann, Ulam's colleague at Los Alamos, was working on the problem of self-replicating systems.
Von Neumann's initial design was founded upon the notion of one robot
building another robot. This design is known as the kinematic model.
As he developed this design, von Neumann came to realize the great
difficulty of building a self-replicating robot, and of the great cost
in providing the robot with a "sea of parts" from which to build its
replicant. Neumann wrote a paper entitled "The general and logical
theory of automata" for the Hixon Symposium in 1948. Ulam was the one who suggested using a discrete system for creating a reductionist model of self-replication.
Ulam and von Neumann created a method for calculating liquid motion in
the late 1950s. The driving concept of the method was to consider a
liquid as a group of discrete units and calculate the motion of each
based on its neighbors' behaviors. Thus was born the first system of cellular automata. Like Ulam's lattice network, von Neumann's cellular automata are two-dimensional, with his self-replicator implemented algorithmically. The result was a universal copier and constructor
working within a cellular automaton with a small neighborhood (only
those cells that touch are neighbors; for von Neumann's cellular
automata, only orthogonal cells), and with 29 states per cell. Von Neumann gave an existence proof
that a particular pattern would make endless copies of itself within
the given cellular universe by designing a 200,000 cell configuration
that could do so. This design is known as the tessellation model, and is called a von Neumann universal constructor.
Motivated by questions in mathematical logic and in part by work on simulation games by Ulam, among others, John Conway
began doing experiments in 1968 with a variety of different
two-dimensional cellular automaton rules. Conway's initial goal was to
define an interesting and unpredictable cellular automaton. According to Martin Gardner,
Conway experimented with different rules, aiming for rules that would
allow for patterns to "apparently" grow without limit, while keeping it
difficult to prove that any given pattern would do so. Moreover,
some "simple initial patterns" should "grow and change for a
considerable period of time" before settling into a static configuration
or a repeating loop. Conway later wrote that the basic motivation for Life was to create a "universal" cellular automaton.
The game made its first public appearance in the October 1970 issue of Scientific American, in Martin Gardner's "Mathematical Games" column, which was based on personal conversations with Conway. Theoretically, the Game of Life has the power of a universal Turing machine: anything that can be computed algorithmically can be computed within the Game of Life. Gardner wrote, "Because of Life's analogies with the rise, fall and
alterations of a society of living organisms, it belongs to a growing
class of what are called 'simulation games' (games that resemble
real-life processes)."
Since its publication, the Game of Life has attracted much
interest because of the surprising ways in which the patterns can
evolve. It provides an example of emergence and self-organization. A version of Life that incorporates random fluctuations has been used in physics to study phase transitions and nonequilibrium dynamics. The game can also serve as a didactic analogy,
used to convey the somewhat counter-intuitive notion that design and
organization can spontaneously emerge in the absence of a designer. For
example, philosopher Daniel Dennett
has used the analogy of the Game of Life "universe" extensively to
illustrate the possible evolution of complex philosophical constructs,
such as consciousness and free will, from the relatively simple set of deterministic physical laws which might govern our universe.
The popularity of the Game of Life was helped by its coming into
being at the same time as increasingly inexpensive computer access. The
game could be run for hours on these machines, which would otherwise
have remained unused at night. In this respect, it foreshadowed the
later popularity of computer-generated fractals. For many, the Game of Life was simply a programming challenge: a fun way to use otherwise wasted CPU
cycles. For some, however, the Game of Life had more philosophical
connotations. It developed a cult following through the 1970s and
beyond; current developments have gone so far as to create theoretic
emulations of computer systems within the confines of a Game of Life
board.
Examples of patterns
Many
different types of patterns occur in the Game of Life, which are
classified according to their behaviour. Common pattern types include: still lifes, which do not change from one generation to the next; oscillators, which return to their initial state after a finite number of generations; and spaceships, which translate themselves across the grid.
The earliest interesting patterns in the Game of Life were
discovered without the use of computers. The simplest still lifes and
oscillators were discovered while tracking the fates of various small
starting configurations using graph paper, blackboards, and physical game boards, such as those used in Go. During this early research, Conway discovered that the R-pentomino
failed to stabilize in a small number of generations. In fact, it takes
1103 generations to stabilize, by which time it has a population of 116
and has generated six escaping gliders; these were the first spaceships ever discovered.
Frequently occurring
examples (in that they emerge frequently from a random starting
configuration of cells) of the three aforementioned pattern types are
shown below, with live cells shown in black and dead cells in white. Period refers to the number of ticks a pattern must iterate through before returning to its initial configuration.
Still lifes
Block
Bee- hive
Loaf
Boat
Tub
Oscillators
Blinker (period 2)
Toad (period 2)
Beacon (period 2)
Pulsar (period 3)
Penta- decathlon (period 15)
Spaceships
Glider
Light- weight spaceship (LWSS)
Middle- weight spaceship (MWSS)
Heavy- weight spaceship (HWSS)
The pulsar
is the most common period-3 oscillator. The great majority of naturally
occurring oscillators have a period of 2, like the blinker and the
toad, but oscillators of many periods are known to exist, and oscillators of periods 4, 8, 14, 15, 30, and a few others have been seen to arise from random initial conditions. Patterns which evolve for long periods before stabilizing are called Methuselahs, the first-discovered of which was the R-pentomino. Diehard
is a pattern that eventually disappears, rather than stabilizing, after
130 generations, which is conjectured to be maximal for patterns with
seven or fewer cells. Acorn takes 5206 generations to generate 633 cells, including 13 escaped gliders.
The R-pentomino
Diehard
Acorn
Conway originally conjectured that no pattern can grow
indefinitely—i.e. that for any initial configuration with a finite
number of living cells, the population cannot grow beyond some finite
upper limit. In the game's original appearance in "Mathematical Games",
Conway offered a prize of fifty dollars to the first person who could
prove or disprove the conjecture before the end of 1970. The prize was
won in November by a team from the Massachusetts Institute of Technology, led by Bill Gosper;
the "Gosper glider gun" produces its first glider on the 15th
generation, and another glider every 30th generation from then on. For
many years, this glider gun was the smallest one known.
In 2015, a gun called the "Simkin glider gun", which releases a glider
every 120th generation, was discovered that has fewer live cells but
which is spread out across a larger bounding box at its extremities.
Gosper glider gun
Simkin glider gun
Smaller patterns were later found that also exhibit infinite growth.
All three of the patterns shown below grow indefinitely. The first two
create a single block-laying switch engine: a configuration that leaves behind two-by-two still life blocks as it translates itself across the game's universe. The third configuration creates two such patterns. The first has only ten live cells, which has been proven to be minimal. The second fits in a five-by-five square, and the third is only one cell high.
Later discoveries included other guns, which are stationary, and which produce gliders or other spaceships; puffer trains, which move along leaving behind a trail of debris; and rakes, which move and emit spaceships. Gosper also constructed the first pattern with an asymptotically optimalquadratic growth rate, called a breeder or lobster, which worked by leaving behind a trail of guns.
It is possible for gliders to interact with other objects in
interesting ways. For example, if two gliders are shot at a block in a
specific position, the block will move closer to the source of the
gliders. If three gliders are shot in just the right way, the block will
move farther away. This sliding block memory can be used to simulate a counter. It is possible to construct logic gates such as AND, OR, and NOT using gliders. It is possible to build a pattern that acts like a finite-state machine connected to two counters. This has the same computational power as a universal Turing machine, so the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints; it is Turing complete. In fact, several different programmable computer architectures have been implemented in the Game of Life, including a pattern that simulates Tetris.
Furthermore, a pattern can contain a collection of guns that fire
gliders in such a way as to construct new objects, including copies of
the original pattern. A universal constructor can be built which
contains a Turing complete computer, and which can build many types of
complex objects, including more copies of itself.
In 2018, the first truly elementary knightship, Sir Robin, was discovered by Adam P. Goucher. A knightship is a spaceship that moves two squares left for every one square it moves down (like a knight in chess),
as opposed to moving orthogonally or along a 45° diagonal. This is the
first new spaceship movement pattern for an elementary spaceship found
in forty-eight years. "Elementary" means that it cannot be decomposed
into smaller interacting patterns such as gliders and still lifes.
Undecidability
Many
patterns in the Game of Life eventually become a combination of still
lifes, oscillators, and spaceships; other patterns may be called
chaotic. A pattern may stay chaotic for a very long time until it
eventually settles to such a combination.
The Game of Life is undecidable,
which means that given an initial pattern and a later pattern, no
algorithm exists that can tell whether the later pattern is ever going
to appear. This is a corollary of the halting problem: the problem of determining whether a given program will finish running or continue to run forever from an initial input.
Indeed, since the Game of Life includes a pattern that is equivalent to a universal Turing machine
(UTM), this deciding algorithm, if it existed, could be used to solve
the halting problem by taking the initial pattern as the one
corresponding to a UTM plus an input, and the later pattern as the one
corresponding to a halting state of the UTM. It also follows that some
patterns exist that remain chaotic forever. If this were not the case,
one could progress the game sequentially until a non-chaotic pattern
emerged, then compute whether a later pattern was going to appear.
Self-replication
On
May 18, 2010, Andrew J. Wade announced a self-constructing pattern,
dubbed "Gemini", that creates a copy of itself while destroying its
parent.
This pattern replicates in 34 million generations, and uses an
instruction tape made of gliders oscillating between two stable
configurations made of Chapman–Greene construction arms. These, in turn,
create new copies of the pattern, and destroy the previous copy. Gemini
is also a spaceship, and is the first spaceship constructed in the Game
of Life that is an oblique spaceship, which is a spaceship that is
neither orthogonal nor purely diagonal. In December 2015, diagonal versions of the Gemini were built.
On November 23, 2013, Dave Greene built the first replicator in the Game of Life that creates a complete copy of itself, including the instruction tape.
In October 2018, Adam P. Goucher finished his construction of the
0E0P metacell, a metacell capable of self-replication. This differed
from previous metacells, such as the OTCA metapixel by Brice Due, which
only worked with already constructed copies near them. The 0E0P metacell
works by using construction arms to create copies that simulate the
programmed rule. The actual simulation of the Game of Life or other Moore neighbourhood rules is done by simulating an equivalent rule using the von Neumann neighbourhood with more states.
The name 0E0P is short for "Zero Encoded by Zero Population", which
indicates that instead of a metacell being in an "off" state simulating
empty space, the 0E0P metacell removes itself when the cell enters that
state, leaving a blank space.
Iteration
From
most random initial patterns of living cells on the grid, observers
will find the population constantly changing as the generations tick by.
The patterns that emerge from the simple rules may be considered a form
of mathematical beauty.
Small isolated subpatterns with no initial symmetry tend to become
symmetrical. Once this happens, the symmetry may increase in richness,
but it cannot be lost unless a nearby subpattern comes close enough to
disturb it. In a very few cases, the society eventually dies out, with
all living cells vanishing, though this may not happen for a great many
generations. Most initial patterns eventually burn out, producing either
stable figures or patterns that oscillate forever between two or more
states;
many also produce one or more gliders or spaceships that travel
indefinitely away from the initial location. Because of the
nearest-neighbour based rules, no information can travel through the
grid at a greater rate than one cell per unit time, so this velocity is
said to be the cellular automaton speed of light and denoted c.
Algorithms
Early
patterns with unknown futures, such as the R-pentomino, led computer
programmers to write programs to track the evolution of patterns in the
Game of Life. Most of the early algorithms
were similar: they represented the patterns as two-dimensional arrays
in computer memory. Typically, two arrays are used: one to hold the
current generation, and one to calculate its successor. Often 0 and 1
represent dead and live cells, respectively. A nested for loop
considers each element of the current array in turn, counting the live
neighbours of each cell to decide whether the corresponding element of
the successor array should be 0 or 1. The successor array is displayed.
For the next iteration, the arrays may swap roles so that the successor
array in the last iteration becomes the current array in the next
iteration, or one may copy the values of the second array into the first
array then update the second array from the first array again.
A variety of minor enhancements to this basic scheme are
possible, and there are many ways to save unnecessary computation. A
cell that did not change at the last time step, and none of whose
neighbours changed, is guaranteed not to change at the current time step
as well, so a program that keeps track of which areas are active can
save time by not updating inactive zones.
To avoid decisions and branches in the counting loop, the rules can be rearranged from an egocentric
approach of the inner field regarding its neighbours to a scientific
observer's viewpoint: if the sum of all nine fields in a given
neighbourhood is three, the inner field state for the next generation
will be life; if the all-field sum is four, the inner field retains its
current state; and every other sum sets the inner field to death.
To save memory, the storage can be reduced to one array plus two
line buffers. One line buffer is used to calculate the successor state
for a line, then the second line buffer is used to calculate the
successor state for the next line. The first buffer is then written to
its line and freed to hold the successor state for the third line. If a toroidal
array is used, a third buffer is needed so that the original state of
the first line in the array can be saved until the last line is
computed.
Glider gun within a toroidal array. The stream of gliders eventually wraps around and destroys the gun.
Red glider on the square lattice with periodic boundary conditions
In principle, the Game of Life field is infinite, but computers have
finite memory. This leads to problems when the active area encroaches on
the border of the array. Programmers have used several strategies to
address these problems. The simplest strategy is to assume that every
cell outside the array is dead. This is easy to program but leads to
inaccurate results when the active area crosses the boundary. A more
sophisticated trick is to consider the left and right edges of the field
to be stitched together, and the top and bottom edges also, yielding a toroidal
array. The result is that active areas that move across a field edge
reappear at the opposite edge. Inaccuracy can still result if the
pattern grows too large, but there are no pathological edge effects.
Techniques of dynamic storage allocation may also be used, creating
ever-larger arrays to hold growing patterns. The Game of Life on a
finite field is sometimes explicitly studied; some implementations, such
as Golly,
support a choice of the standard infinite field, a field infinite only
in one dimension, or a finite field, with a choice of topologies such as
a cylinder, a torus, or a Möbius strip.
Alternatively, programmers may abandon the notion of representing
the Game of Life field with a two-dimensional array, and use a
different data structure, such as a vector of coordinate pairs
representing live cells. This allows the pattern to move about the field
unhindered, as long as the population does not exceed the size of the
live-coordinate array. The drawback is that counting live neighbours
becomes a hash-table lookup or search operation, slowing down simulation
speed. With more sophisticated data structures this problem can also be
largely solved.
For exploring large patterns at great time depths, sophisticated algorithms such as Hashlife
may be useful. There is also a method for implementation of the Game of
Life and other cellular automata using arbitrary asynchronous updates
whilst still exactly emulating the behaviour of the synchronous game. Source code examples that implement the basic Game of Life scenario in various programming languages, including C, C++, Java and Python can be found at Rosetta Code.
Since the Game of Life's inception, new, similar cellular automata
have been developed. The standard Game of Life is symbolized as B3/S23. A
cell is born if it has exactly three neighbours, survives if it has two
or three living neighbours, and dies otherwise. The first number, or
list of numbers, is what is required for a dead cell to be born. The
second set is the requirement for a live cell to survive to the next
generation. Hence B6/S16 means "a cell is born if there are six
neighbours, and lives on if there are either one or six neighbours".
Cellular automata on a two-dimensional grid that can be described in
this way are known as Life-like cellular automata. Another common Life-like automaton, Highlife,
is described by the rule B36/S23, because having six neighbours, in
addition to the original game's B3/S23 rule, causes a birth. HighLife is
best known for its frequently occurring replicators.
Additional Life-like cellular automata exist. The vast majority of these 218 different rules
produce universes that are either too chaotic or too desolate to be of
interest, but a large subset do display interesting behavior. A further
generalization produces the isotropic rulespace, with 2102 possible cellular automaton rules
(the Game of Life again being one of them). These are rules that use
the same square grid as the Life-like rules and the same eight-cell
neighbourhood, and are likewise invariant under rotation and reflection.
However, in isotropic rules, the positions of neighbour cells relative
to each other may be taken into account in determining a cell's future
state—not just the total number of those neighbours.
A
sample of a 48-step oscillator along with a 2-step oscillator and a
4-step oscillator from a two-dimensional hexagonal Game of Life (rule
H:B2/S34)
Some variations on the Game of Life modify the geometry of the
universe as well as the rule. The above variations can be thought of as a
two-dimensional square, because the world is two-dimensional and laid
out in a square grid. One-dimensional square variations, known as elementary cellular automata, and three-dimensional square variations have been developed, as have two-dimensional hexagonal and triangular variations. A variant using aperiodic tiling grids has also been made.
Conway's rules may also be generalized such that instead of two states, live and dead,
there are three or more. State transitions are then determined either
by a weighting system or by a table specifying separate transition rules
for each state; for example, Mirek's Cellebration's multi-coloured
Rules Table and Weighted Life rule families each include sample rules
equivalent to the Game of Life.
Patterns relating to fractals and fractal systems may also be
observed in certain Life-like variations. For example, the automaton
B1/S12 generates four very close approximations to the Sierpinski triangle
when applied to a single live cell. The Sierpinski triangle can also be
observed in the Game of Life by examining the long-term growth of an
infinitely long single-cell-thick line of live cells, as well as in Highlife, Seeds (B2/S), and Wolfram's Rule 90.
Immigration is a variation that is very similar to the Game of Life, except that there are two on
states, often expressed as two different colours. Whenever a new cell
is born, it takes on the on state that is the majority in the three
cells that gave it birth. This feature can be used to examine
interactions between spaceships and other objects within the game.
Another similar variation, called QuadLife, involves four different on
states. When a new cell is born from three different on neighbours, it
takes the fourth value, and otherwise, like Immigration, it takes the
majority value. Except for the variation among on cells, both of these variations act identically to the Game of Life.
Music
Various musical composition techniques use the Game of Life, especially in MIDI sequencing. A variety of programs exist for creating sound from patterns generated in the Game of Life.
Notable programs
The 6366548773467669985195496000th (6×1027) generation of a Turing machine, made in the game of Life, computed in less than 30 seconds on an Intel Core Duo 2 GHz CPU using Golly in Hashlife mode
Computers have been used to follow Game of Life configurations since
it was first publicized. When John Conway was first investigating how
various starting configurations developed, he tracked them by hand using
a go
board with its black and white stones. This was tedious and prone to
errors. The first interactive Game of Life program was written in an
early version of ALGOL 68C for the PDP-7 by M. J. T. Guy and S. R. Bourne. The results were published in the October 1970 issue of Scientific American, along with the statement: "Without its help, some discoveries about the game would have been difficult to make."
A color version of the Game of Life was written by Ed Hall in 1976 for Cromemco microcomputers, and a display from that program filled the cover of the June 1976 issue of Byte. The advent of microcomputer-based color graphics from Cromemco has been credited with a revival of interest in the game.
Two early implementations of the Game of Life on home computers were by Malcolm Banthorpe written in BBC BASIC. The first was in the January 1984 issue of Acorn User magazine, and Banthorpe followed this with a three-dimensional version in the May 1984 issue. Susan Stepney, Professor of Computer Science at the University of York, followed this up in 1988 with Life on the Line, a program that generated one-dimensional cellular automata.
There are now thousands of Game of Life programs online, so a
full list will not be provided here. The following is a small selection
of programs with some special claim to notability, such as popularity or
unusual features. Most of these programs incorporate a graphical user
interface for pattern editing and simulation, the capability for
simulating multiple rules including the Game of Life, and a large
library of interesting patterns in the Game of Life and other cellular
automaton rules.
Golly
is a cross-platform (Windows, Macintosh, Linux, iOS, and Android)
open-source simulation system for the Game of Life and other cellular
automata (including all Life-like cellular automata, the Generations
family of cellular automata from Mirek's Cellebration, and John von
Neumann's 29-state cellular automaton) by Andrew Trevorrow and Tomas
Rokicki. It includes the Hashlife algorithm for extremely fast
generation, and Lua or Python scriptability for both editing and simulation.
Mirek's Cellebration is a freeware one- and two-dimensional cellular
automata viewer, explorer, and editor for Windows. It includes powerful
facilities for simulating and viewing a wide variety of cellular
automaton rules, including the Game of Life, and a scriptable editor.
Xlife is a cellular-automaton laboratory by Jon Bennett. The
standard UNIX X11 Game of Life simulation application for a long time,
it has also been ported to Windows. It can handle cellular automaton
rules with the same neighbourhood as the Game of Life, and up to eight
possible states per cell.
Dr. Blob's Organism is a Shoot 'em up
based on Conway's Life. In the game, Life continually generates on a
group of cells within a "petri dish". The patterns formed are smoothed
and rounded to look like a growing amoeba spewing smaller ones (actually
gliders). Special "probes" zap the "blob" to keep it from overflowing
the dish while destroying its nucleus.
Google implemented an easter egg of the Game of Life in 2012. Users who search for the term are shown an implementation of the game in the search results page.
I believe that abortion care is a positive social good—and I think it’s time people said so.
Not long ago, the Daily Kos published an article titled “I
Am Pro-Choice, Not Pro-Abortion.” “Has anyone ever truly been
pro-abortion?” one commenter asked.
Uh. Yes. Me. That would be me.
I am pro-abortion like I’m pro–knee replacement and pro-chemotherapy
and pro–cataract surgery. As the last protection against ill-conceived
childbearing when all else fails, abortion is part of a set of tools
that help women and men to form the families of their choosing. I
believe that abortion care is a positive social good. And I suspect that
a lot of other people secretly believe the same thing. I think it’s
time we said so.
Note: I’m also pro-choice. Choice is about who gets to make the
decision. The question of whether and when we bring a new life into the
world is, to my mind, one of the most important decisions a person can
make. It is too big a decision for us to make for each other, especially
for perfect strangers.
But independent of who owns the decision, I’m pro on the procedure.
I’ve decided that it’s time, for once and for all, to count it out on my
ten fingers.
I’m pro-abortion because being able to delay and limit childbearing
is fundamental to female empowerment and equality. A woman who lacks the
means to manage her fertility lacks the means to manage her life. Any
plans, dreams, aspirations, responsibilities or commitments—no matter
how important—have a great big contingency clause built-in: “… until or
unless I get pregnant, in which case all bets are off.” Think of any
professional woman you know. She wouldn’t be in that role if she hadn’t
been able to time and limit her childbearing. Think of any girl you know
who imagines becoming a professional woman. She won’t get there unless
she has effective, reliable means to manage her fertility. In
generations past, nursing care was provided by nuns and teachers who
were spinsters, because avoiding sexual intimacy was the only way women
could avoid unpredictable childbearing and so be freed up to serve their
communities in other capacities. But if you think that abstinence
should be our model for modern fertility management, consider the little
graves that get found every so often under old nunneries and Catholic
homes for unwed mothers.
I’m pro-abortion because well-timed pregnancies give children a
healthier start in life. We now have ample evidence that babies do best
when women are able to space their pregnancies and get both prenatal and
preconception care. The specific nutrients we ingest in the weeks
before we get pregnant can have a lifelong effect on the well-being of
our offspring. Rapid repeat pregnancies increase the risk of low
birth-weight babies and other complications. Wanted babies are more
likely to get their toes kissed, to be welcomed into families that are
financially and emotionally ready to receive them, to get preventive
medical care during childhood, and to receive the kinds of loving
engagement that helps young brains to develop.
I’m pro-abortion because I take motherhood seriously. Most female
bodies can incubate a baby; thanks to antibiotics, cesareans, and
anti-hemorrhage drugs, most of us are able to survive pushing a baby out
into the world. But parenting is a lot of work, and doing it well takes
twenty dedicated years of focus, attention, patience, persistence,
social support, mental health, money, and a whole lot more. This is the
biggest, most life-transforming thing most of us will ever do. The idea
that women should simply go with it when they find themselves pregnant
after a one-night stand, or a rape, or a broken condom completely trivializes motherhood.
I’m pro-abortion because intentional childbearing helps couples,
families, and communities to get out of poverty. Decades of research in
countries ranging from the United States to Bangladesh show that
reproductive policy is economic policy. It is no coincidence that the
American middle class rose along with the ability of couples to plan
their families, starting at the beginning of the last century. Having
two or three kids instead of eight or ten was critical to prospering in
the modern industrial economy. Early, unsought childbearing nukes
economic opportunity and contributes to multigenerational poverty. Today
in the United States, unsought pregnancy and childbearing is declining
for everyone but the poorest families and communities, contributing to
what some call a growing “caste system” in America. Strong, determined
girls and women sometimes beat the odds, but their stories inspire us
precisely because they are the exceptions to the rule. Justice dictates
that the full range of fertility management tools—including the best
state-of-the-art contraceptive technologies and, when that fails,
abortion care—be equally available to all, not just a privileged few.
I’m pro-abortion because reproduction is a highly imperfect process.
Genetic recombination is a complicated progression with flaws and false
starts at every step along the way. To compensate, in every known
species including humans, reproduction operates as a big funnel. Many
more eggs and sperm are produced than will ever meet; more combine into
embryos than will ever implant; more implant than will grow into babies;
and more babies are born than will grow up to have babies of their own.
This systematic culling makes God or nature the world’s biggest
abortion provider: nature’s way of producing healthy kids essentially
requires every woman to have an abortion mill built into her own body.
In humans, an estimated 60 to 80 percent of fertilized eggs
self-destruct before becoming babies, which is why the people who kill
the most embryos are those like the Duggars who try to maximize their
number of pregnancies. But the weeding-out process is also highly
imperfect. Sometimes perfectly viable combinations boot themselves out;
sometimes horrible defects slip through. A woman’s body may be less
fertile when she is stressed or ill or malnourished, but as pictures of
skeletal moms and babies show, some women conceive even under
devastating circumstances. Like any other medical procedure, therapeutic
contraception and abortion complement natural processes designed to
help us survive and thrive.
I’m pro-abortion because I think morality is about the well-being of
sentient beings. I believe that morality is about the lived experience
of sentient beings—beings who can feel pleasure and pain, preference and
intention and who at their most complex can live in relation to other
beings, love and be loved, and value their own existence. What are they
capable of wanting? What are they capable of feeling? These are the
questions my husband and I explored with our children when they were
figuring out their responsibility to their chickens and guinea pigs. It
was a lesson that turned expensive when the girls stopped drinking milk
from cows that didn’t get to see the light of day or eat grass, but it’s
not one I regret. Do unto others as they want you to do unto them. It’s
called the “Platinum Rule.” In this moral universe, real people count
more than potential people, hypothetical people, or corporate people.
I’m pro-abortion because contraceptives are imperfect, and people
are too. The pill is 1960s technology, now half a century old. For
decades, women were told that the pill was 99 percent effective, and
they blamed themselves when they got pregnant anyway. But that 99
percent is a “perfect use” statistic. In the real world, where most of
us live, people aren’t perfect. In the real world, one in eleven women
relying on the pill gets pregnant each year. For a couple relying on
condoms, that’s one in six. Young and poor women—those whose lives are
least predictable and most vulnerable to being thrown off course—are
also those who have the most difficulty taking pills consistently. Pill
technology most fails those who need it most, which makes abortion
access a matter not only of compassion but of justice. State-of-the-art
IUDs and implants radically change this equation, largely because they
take human error out of the picture for years on end, or until a woman
wants a baby. And despite the deliberate misinformation being spread by
opponents, these methods are genuine contraceptives, not abortifacients.
Depending on the method chosen, they disable sperm or block their path,
or prevent an egg from being released. Once settled into place, an IUD
or implant drops the annual pregnancy rate below one in five hundred.
And guess what? Teen pregnancies and abortions plummet—which makes me
happy, because even though I’m pro-abortion, I’d love the need for
abortion to go away. Why mitigate harm when you can prevent it?
I’m pro-abortion because I believe in mercy, grace, compassion, and
the power of fresh starts. Many years ago, my friend Chip was driving
his family on vacation when his kids started squabbling. His wife,
Marla, undid her seatbelt to help them, and, as Chip looked over at her,
their top-heavy minivan veered onto the shoulder and then rolled, and
Marla died. Sometimes people make mistakes or have accidents that they
pay for the rest of their lives. But I myself have swerved onto the
shoulder and simply swerved back. The price we pay for a lapse in
attention or judgment or an accident of any kind isn’t proportional to
the error we made. Who among us hasn’t had unprotected sex when the time
or situation or partnership wasn’t quite right for bringing a new life
into the world? Most of the time we get lucky; sometimes we don’t. And
in those situations we rely on the mercy, compassion, and generosity of
others. In this regard, an unsought pregnancy is like any other
accident. I can walk today only because surgeons reassembled my lower
leg after it was crushed between the front of a car and a bicycle frame
when I was a teen. And I can walk today (and run and jump) because
another team of surgeons reassembled my knee joint after I fell off a
ladder. And I can walk today (and bicycle with my family) because a
third team of surgeons repaired my other knee after I pulled a whirring
brush mower onto myself, cutting clear through bone. Three accidents,
all my own doing, and three knee surgeries. Some women have three
abortions.
I’m pro-abortion because the future is always in motion, and we have
the power and responsibility to shape it well. As a college student, I
read a Ray Bradbury story about a man who travels back into prehistory
on a “time safari.” The tourists have been coached about the importance
of not disturbing anything lest they change the flow of history. When
they return to the present, they realize that the outcome of an election
has changed, and they discover that the protagonist, who had gone off
the trail, has a crushed butterfly on the bottom of his shoe. In
baby-making, as in Bradbury’s story, the future is always in motion, and
every little thing we do has consequences we have no way to predict.
Any small change means that a different child comes into the world.
Which nights your mother had headaches, the sexual position of your
parents when they conceived you, whether or not your mother rolled over
in bed afterward—if any of these things had been different, someone else
would be here instead of you. Every day, men and women make small
choices and potential people wink into and out of existence. We move,
and our movements ripple through time in ways that are incomprehensible,
and we can never know what the alternate futures might have been. But
some things we can know or predict, at least at the level of
probability, and I think this knowledge provides a basis for guiding
wise reproductive decisions. My friend Judy says that parenting begins
before conception. I agree. How and when we choose to carry forward a
new life can stack the odds in favor of our children or against them,
and to me that is a sacred trust.
I’m pro-abortion because I love my daughter. I first wrote the story
of my own abortion when Dr. George Tiller was murdered, and I couldn’t
bear the thought of abortion providers standing in the crosshairs alone.
“My Abortion Baby” was about my daughter, Brynn, who exists only
because a kind doctor such as George Tiller gave me and my husband the
gift of a fresh start when we learned that our wanted pregnancy was
unhealthy. Brynn literally embodies the ever-changing flow of the
future, because she could not exist in an alternate universe in which I
would have carried that first pregnancy to term. She was conceived while
I would still have been pregnant with a child we had begun to imagine
but who never came to be. My husband and I felt very clear that carrying
forward that pregnancy would have been a violation of our values, and
neither of us ever second-guessed our decision. Even so, I grieved. Even
when I got pregnant again a few months later, I remember feeling
petulant and thinking, I want that baby, not this one. And then Brynn came out into the world, and I looked into her eyes, fell in love, and never looked back.
All around us living, breathing, and loving are the chosen children
of mothers who waited, who ended an ill-timed or unhealthy pregnancy and
then later chose to carry forward a new life. “I was only going to have
two children,” my friend Jane said as her daughters raced, screeching
joyfully, across my lawn. Jane followed them with her eyes. “My
abortions let me have these two when the time was right, with someone I
loved.”
Those who see abortion as an unmitigated evil often talk about the
“millions of missing people” who were not born into this world because a
pregnant woman decided “Not now.” But they never talk about the
millions of children and adults who are here today only because
their mothers had abortions—real people who exist in this version of
the future, people who are living out their lives all around us—loving,
laughing, suffering, struggling, dancing, dreaming, and having babies of
their own.
When those who oppose abortion lament the “missing people,” I hear an echo of my own petulant thought: I want that person, not this one.
And I wish that they could simply experience what I did, that they
could look into the beautiful eyes of the people in front of them and
fall in love.
