Cellular Automata and Cellular Automata and Artificial LifeArtificial Life

Cellular Automata Cellular Automata (( 元胞自动机元胞自动机 ))

Each Unit Is an Automata Connectivity: Each Automata Is

Linked With Its Neighborhood

An example of Cellular An example of Cellular AutomataAutomata

every unit has a value: a, b, c and d.

ab c db c

An example of Cellular AutomataAn example of Cellular Automata

Rule 90

10 0 00 0

Input States

111 110 101 100 011 010 001 000

outputs 0 1 0 1 1 0 1 0

An example of Cellular AutomataAn 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 States

111 110 101 100 011 010 001 000

outputs 0 1 0 1 1 0 1 0

An example of Cellular AutomataAn 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 attractorsStrong attractors

Rule 250: all 1Rule 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 attractorsShort-period attractors

Rule 108 and 178: periods of 1 or 2.

long-period attractorslong-period attractors

Rule 90 and 126: too long to be easily observable.

One dimensional cellular One dimensional cellular automata with three inputsautomata with three inputs

One dimension ( two dimensions )With three inputs ( with more than 3 inputs)Neighbors: 3, 5, …

The nearest neighbors

One dimensional cellular One dimensional cellular automata with two inputsautomata with two inputs

Even-numbered automata;Odd-numbered automata;

TT+1T+2

One dimensional cellular One dimensional cellular automata with two inputsautomata with two inputs

Code LR LR LR LR Left and right inputs

00 01 10 11 Input configuration

0 0 0 0 0

1 0 0 0 1 AND

2 0 0 1 0 Unsymmetrical

3 0 0 1 1 Transmits left input

4 0 1 0 0 Unsymmetrical

5 0 1 0 1 Transmits right input

6 0 1 1 0 XOR

7 0 1 1 1 OR

Two-dimensionalTwo-dimensional Cellular Cellular AutomataAutomata

The first cellular automata proposed by von Neumann were on the nodes of a two-dimensional 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 Automata2D Cellular Automata

The grid is infinite. When it has edges, we connect the right edge of

the figure to the left edge; ……

2D Cellular Automata2D 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 neighborhoodTwo kinds of neighborhood

Von Neumann neighmorhood (left) k=5Moore neighborhood (right) k=9

2D threshold automata2D threshold automata

Threshold t: -1 <= t <= k+1New State = 1 iff S >= t.

S: the sum of the states of the neighbors

If T is small or largeIf 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=5T =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=5T =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=5T =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=5T =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 Window Automata and Dendritic GrowthGrowth

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 growthIt 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”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 lifeGame of life

Square

Game of lifeGame of life

honeycomb

Game of lifeGame of life

HoneycombGlider

Game of lifeGame 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”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 LifeArtificial LifeBoidsFloysGame of lifeLife exists in computer?

Artificial LifeArtificial LifeWhat is life?Can we study and research life in other media

instead of proteins?

Selfproducing

Evolutionary

...

Artificial LifeArtificial LifeArtificial 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 LifeArtificial LifeLife “as we know it”; 生命如我所知 Life "as it could be“; 生命如其所能 .

Artificial LifeArtificial LifeCellullar AutomataGenetic Algorithms

-evolutionary computationSocieties and Collective BehaviorVirtual WorldsArtificial brainRobots

Societies and Collective Societies and Collective BehaviorBehavior

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 Societies and Collective BehaviorBehavior

-boids

-floys

-artificial socialty

-artificial ecology

-artificial fishes

Artificial Life- Societies and Artificial Life- Societies and Collective BehaviorCollective 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

RobotsRobotsConstruction of adaptive autonomous robots;

-The robotic agent interacts with its environment and learns from this interaction, leading to emergent robotic behavior;

Virtual WorldsVirtual WorldsArtificial treesArtificial fishes

Artificial LifeArtificial Lifeeconomics

Artificial Life

Ecology

Neuroscience

Biology and medicines

EngineeringSocialogy

and psycology

Artificial LifeArtificial LifeArtificial

Intelligence

Artificial Life

Neural networks

Evolutionary computing

Graphics and computer animation

Engineering

Artificial LifeArtificial LifeThe way to study and research the complex

systems.Truly interdisciplinary fields: biology,

chemistry and physics to computer science and engineering.

Open problemsOpen 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 problemsOpen 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 problemsOpen 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 problemsOpen 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 systemL system

同时使用产生式规则： 如： a→ab, b→abaababaabaababaababa

龟几何龟几何 (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 :

龟几何龟几何

F: 向前移动步长 d, 新状态 :(x 1, y1, α)X1 = x + cosα * dY1 = y + sinα* d在点 (x,y) 与 (x 1, y1) 之间画一条线。

α

(x1,y1)

(x,y)

龟几何龟几何

f: 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)

龟几何龟几何 举例： w: F-F-F-F, δ=90

P: F→F-F+F+FF-F-F+F

龟几何龟几何 举例： δ=25.7

w: F

P: F→F[+F]F[-F]F

Artificial LifeArtificial 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 LifeArtificial LifeSimulating simple populations of self-

replicating 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.