Cellular Automata and Artificial
Life
Cellular Automata
(元胞自动机)


Each Unit Is an Automata
Connectivity: Each Automata Is
Linked With Its Neighborhood
An example of Cellular
Automata

every unit has a value: a, b, c and d.
b
a
c
b
d
c
An example of Cellular Automata
0
1
Input
111 110
States
outputs 0
1

Rule 90
0
0
0
0
101 100 011 010
001 000
0
1
1
1
0
0
An example of Cellular Automata

There are 2^3=8 different input states.
 There are 2^8 =256 different state change rules.
 Each rule is numbered from 0 to 255.
Input
111 110
States
outputs 0
1
101 100 011 010
001 000
0
1
1
1
0
0
An example of Cellular Automata

See the pictures of the dynamics of these
rules.
 Text book:
Gerard Weisbuch, Complex Systems
Dynamics, an introduction to automata
networks, Addison-Wesley Publishing
Company, Inc. USA. P25-P27
Strong attractors

Rule 250: all 1
 Rule 128: all configurations with at least
one 0 converge toward the attractor
containing only 0’s, ( exception of
configuration of all 1’s )
Short-period attractors

Rule 108 and 178: periods of 1 or 2.
long-period attractors

Rule 90 and 126: too long to be easily
observable.
One dimensional cellular
automata with three inputs

One dimension ( two dimensions )
 With three inputs ( with more than 3 inputs)
 Neighbors: 3, 5, …
The nearest neighbors
One dimensional cellular
automata with two inputs

Even-numbered automata;
 Odd-numbered automata;
T
T+1
T+2
One dimensional cellular
automata with two inputs
Code
0
1
LR
00
0
0
LR
01
0
0
LR
10
0
0
LR
11
0
1
2
3
4
0
0
0
0
0
1
1
1
0
0
1
0
5
6
7
0
0
0
1
1
1
0
1
1
1
0
1
Left and right inputs
Input configuration
AND
Unsymmetrical
Transmits left input
Unsymmetrical
Transmits right input
XOR
OR
Two-dimensional Cellular
Automata

The first cellular automata proposed by von
Neumann were on the nodes of a twodimensional square grid.
 Have a relatively ancient history, from von
Neumann’s self-reproducing automata of the
1940’s to Conway’s “game of life”.
2D Cellular Automata

The grid is infinite.
 When it has edges, we connect the right edge of
the figure to the left edge; ……
2D Cellular Automata

Homogeneous: The state change rules are in
principle the same for all of the automata in
the lattice. (inhomogeneous)
 Parallel iteration mode;
 The connectivity structure is related to the
symmetries of the lattice.
Two kinds of neighborhood

Von Neumann neighmorhood (left) k=5
 Moore neighborhood (right) k=9
2D threshold automata

Threshold t: -1 <= t <= k+1
 New State = 1 iff S >= t.
S: the sum of the states of the
neighbors
If T is small or large

Weak thresholds ( T <= 0 or is close
to 0 ) favor the growth of zones of
automata in state 1.
 Strong thresholds ( T is close to k )
favor the growth of zones of automata
in state 0.
T =1.5, k=5

t=0, t=1, t=2, t=3,
t=4 from left to right,
up to bottom.
T =1.5, k=5

Isolated 1’s are destroyed.
 The condition for growth is that at
least two neighbors must be in state 1.
 If the groups of 1’s are far enough
apart, the growth stops when the
convex envelope of the initial
configurations is full of 1’s
T =1.5, k=5

t=0, t=1, t=2, t=3,
t=4 from left to right,
up to bottom.
T =1.5, k=5

A good representation of the growth
of crystals (quartz) in thermodynamic
equilibrium.
 Convex envelope of the seeds
corresponds to the equilibrium shapes.
Window Automata and Dendritic
Growth

If an automaton is in state 1, it stays
there;
 If an automaton is in state 0, it
changes to 1 only if one of its
neighbors is in state 1.
 See a picture.
It modeled snowflake growth

Snowflakes are crystals which undergo
dendritic growth to lacy shapes
 When the solid seed is much colder than
the solution it will grow.
 Not allowing the transition toward the state
1 when the number of neighbors in state 1
is too large because of heat dissipating
Conway’s “game of life”

An automaton in state 0 switches to state 1
if three of its neighbors are in state
1( born ). Otherwise, it stays in state 0.
 An automaton in state 1 stays in state 1 if 2
or 3 of its neighbors are in state 1. It
switches to state 0 in the other cases. ( dies,
either of isolation or of overcrowding ).
Game of life

Square
Game of life

honeycomb
Game of life

Honeycomb
 Glider
Game of life

After four iterations, it returns to its initial
configuration, having undergone a
translation.
 Binary signals that propagate down the
diagonals of the lattice.
 The collision of two gliders destroys them
both.
 See demo
Conway’s “Game of Life”

Experiment to determine if a simple system of
rules could create a universal computer.
 “Universal computer" denotes a machine that
is capable of emulating any kind of
information processing by implementing a
small set of simple operations.
 To find self-reproducing organisms within the
life system
Artificial Life

Boids
 Floys
 Game of life
 Life exists in computer?
Artificial Life

What is life?
 Can we study and research life in other media
instead of proteins?
Selfproducing
Evolutionary
...
Artificial Life

Artificial life study and research human-made
systems that possess some of the essential
properties of life.
 There are many such systems that meet this
criterion—digital ( boids, floys, game of
life, …), and mechanical (robots)
Artificial Life
Life “as we know it”;生命如我所知
 Life "as it could be“;生命如其所能
.

Artificial Life

Cellullar Automata
 Genetic Algorithms
-evolutionary computation
 Societies and Collective Behavior
 Virtual Worlds
 Artificial brain
 Robots
Societies and Collective
Behavior

Attempting to understand high-level behavior
from low-level rules;
 Artificial populations which posses the
behavior of life.
- How the simple rules of Darwinian
evolution lead to high-level structure,
- Or the way in which the simple interactions
between ants and their environment lead to
complex trail-following behavior.
Societies and Collective
Behavior
-boids
-floys
-artificial socialty
-artificial ecology
-artificial fishes
Artificial Life- Societies and
Collective Behavior
 Understanding
this relationship in
particular systems promises to provide
novel solutions to complex real-world
problems, such as disease prevention,
stock-market prediction, and data-mining
on the internet
Robots

Construction of adaptive autonomous robots;
-The robotic agent interacts with its
environment and learns from this interaction,
leading to emergent robotic behavior;
Virtual Worlds

Artificial trees
 Artificial fishes
Artificial Life
Neuroscience
Biology and
medicines
Socialogy
and psycology
economics
Artificial Life
Ecology
Engineering
Artificial Life
Artificial
Intelligence
Evolutionary
computing
Artificial Life
Neural
networks
Graphics and
computer
animation
Engineerin
g
Artificial Life

The way to study and research the complex
systems.
 Truly interdisciplinary fields: biology,
chemistry and physics to computer science
and engineering.
Open problems
生命是如何从非生命的物质中产生的？
 生命系统的潜能和极限是什么？
 生命与心灵（意识）、机器和文化之间有
什么联系？

Open problems
在试管中生成一个大分子原型生命组织
（molecular proto-organism）
 在基于硅的人工化学中完成向生命的转变
 确定最基本的生命组织的存在性
 模拟一个单细胞生物的生命周期
 解释在生命系统中，规则和符号是如何从
物理动力学中产生的

Open problems
确定在无穷尽的生命进化过程中什么是不
可避免的
 确定从特定系统向一般系统进化所必需的
条件
建 立 在 任 何 尺 度 下 合 成 动 态 结 构
（dynamical hierarchy）的形式框架
 确定我们对于生物和生态系统的影响带来
的结果的可预测性

Open problems
发展一套进化系统的信息处理、信息流和
信息生成的理论
 在人工生命系统中演示智能和意识的涌现
 预测机器在下一次生物进化时代的影响
 提供一个量化的文化与生物进化之间联系
的模型
 建立一个关于人工生命的伦理原则

L system
同时使用产生式规则：
 如： a→ab, b→a
b
a
ab
aba
abaab
abaababa

龟几何
(x,y,α)表示龟的状态。(x,y)表示位
置，α表示龟爬行的方向。
 步长：d; 角度增量: δ
 用下面命令控制龟的运动:

龟几何
F: 向前移动步长d, 新状态:(x 1, y1, α)
X1 = x + cosα * d
Y1 = y + sinα* d
在点(x,y)与(x 1, y1)之间画一条线。
(x1,y1)
α
(x,y)
龟几何
向前移动步长d, 不画线。
 +：向左转角度δ，
新状态：(x 1, y1, α+δ)
 -：向右转角度δ，
新状态：(x 1, y1, α-δ)
 f:
龟几何
举例： w: F-F-F-F, δ=90
P: F→F-F+F+FF-F-F+F
龟几何
举例： δ=25.7
w: F
P: F→F[+F]F[-F]F
Artificial Life

is devoted to a new discipline that investigates the scientific,
engineering, philosophical, and social issues involved in our
rapidly increasing technological ability to synthesize life-like
behaviors from scratch in computers, machines, molecules,
and other alternative media. By extending the horizons of
empirical research in biology beyond the territory currently
circumscribed by life-as-we-know-it, the study of artificial life
gives us access to the domain of life-as-it-could-be. Relevant
topics span the hierarchy of biological organization, including
studies of the origin of life, self-assembly, growth and
development, evolutionary and ecological dynamics, animal
and robot behavior, social organization, and cultural evolution.
Artificial Life

Simulating simple populations of selfreplicating entities, examines the abilities and
characteristics of different chemistries in
supporting life-like behavior.
 Both the biochemical and the computational
approaches seek to shed light on the
compelling question of the origin of life.
 The essential of evolution and adaption.
