Chaos and Complex Systems Theories as

rucksackbulgeAI and Robotics

Dec 1, 2013 (3 years and 4 months ago)

54 views

Strategies and Rubrics for Teaching
Chaos and Complex Systems Theories as
Elaborating, Self
-
Organizing, and
Fractionating Evolutionary Systems

Fichter, Lynn S., Pyle, E.J., and Whitmeyer, S.J., 2010,
Journal of Geoscience Education (in press)

Cellular
Automata

Cellular Automata and Self Organization

Cellular

Automata

(CA)

are

simply

grids

of

cells,

where

the

individual

cells

change

states

according

to

a

set

of

rules
.

The

CA

may

be

one

dimensional,

or

linear,

like

a

string

of

cells

in

a

row

(below),

or

two

dimensional,

like

a

checkerboard


Optimal Local Rule Set

Survival

Rules



2
/
3

a

live

cell

survives

to

the

next

generation

if

at

least

2

but

no

more

than

three

of

the

surrounding

8

cells

are

alive
.

Less

than

2

and

it

dies

of

loneliness
;

more

than

3

and

it

dies

of

over

crowding
.
-

Birth

Rules



3
/
3

a

dead

cells

comes

alive

the

next

generation

if

3
,

any

3
,

of

the

surrounding

8

cells

are

also

alive
.

Local Rules/Global
Behavior

1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

?

Now, as cells are added, which
will come alive,

which survive?

Cellular Automata and Self Organization

Classifying Cellular Automata Rules

Stephen Wolfram

Class

One

-

Fixed

or

Static
:

Rules

that

produce

dull

universes,

such

as

all

dead

cells

or

all

living

cells
;

e
.
g
.

ice
.

Class

Two

-

Periodic

or

Oscillatory
:

Rules

that

produce

stable,

repetitive

configurations
.

Class

Three

-

Chaotic
:

Rules

that

produce

chaotic

patterns
;

e
.
g
.

molecules

in

a

gas
.

Class

Four

-

Complexity
:

Rules

that

produce

complex,

locally

organized

patterns
;

e
.
g
.

behave

like

a

flowing

liquid
..

Classifying Cellular Automata Rules

Chris Langton

Power
-
Law
Relationships in Cellular
Automata

Run

a

random

array

until

it

stops,

add

a

live

cell

at

random,

run

again

until

it

stops
.

Avalanche

size

is

the

number

of

generations

from

initiation

until

it

stops
.

Most

avalanches

last

only

one

or

a

few

generations
;

others

may

last

hundreds

of

generations
.

Plotted

up

the

avalanches

follow

a

power
-
law

meaning

Cellular

Automata

(with

optimum

local

rules)

are

S
elf

O
rganized

C
ritical

systems
.

Evolution of Ripples

A cellular automata model

Mechanics of Wind Ripple Stratigraphy

Author(s): Spencer B. Forrest and Peter K. Haff

Source: Science, New Series, Vol. 255, No. 5049 (Mar. 6, 1992), pp. 1240
-
1243

Published by: American Association for the Advancement of Science

Cellular Automata Examples