Design Challenge 3:
Aesthetic of Cellular Automata and Mobile Agents Built Configurations
 
Andrew Adamatzky

Introduction

We are not the first who talks about cellular automata in a context of art,
back in 1990th Andy Wuensche and Chris Langton undertook a series of work-
shops and exhibitions (e.g “Merged Realities Symposium”, University of Ari-
zona, March 4-6, 1999, and an exhibit “Complexity in Small Universes”, in
an art exhibition, and also “Objective Wonder: Data as Art”, see details in
www.ddlab.org). I am also keeping in my office two pieces of cellular-automaton
art, see Fig. 1, as a reminder it is not only virtual things but sometimes we can
even touch it.





The first image is a T-shirt printed in Santa Fe Institute (USA) with graphs of global transitions of one-dimensional cellular automata, generated in Discrete Dynamics Lab by Andy Wuensche. The second image is as coffee table cover produced by mother of Dr. Genaro Martinez (Mexico), this displaysconfiguration of two-dimensional automaton, starting its developing with only one non-resting site.

During theWorkshop we aim to undertake an exhaustive search of simple CA
and mobile agents rules to select rules that generate configurations appealing in
a tasteful way, e.g. being sexy, cool or freaky but never dull.

Step 1: Defining the Models

The CA Model

We study two-dimensional cellular automaton where every cell  (grid location)
Can be in one of two states. It is either off  (sometimes called 0 and visualized as white space) or it is on (sometimes called the 1 state and visualized as black space).

At each step it updates its own state depending on the number of black squares in its neigburhood. The neighbourhood in this case is the eight squares around the cell in question. (Think of the places an unrestricted King could move to in the middle of a chessboard, this defines the neighbourhood).

We also use 4 natural numbers, which vary between 1 and 8. Each different combination gives a different system. Let us call these numbers as follows.

M1, M2, N1, N2

At each step:

any white cell (i.e. in state 0)  switches to black (state 1) if the number of black neighbours is between M1 and M2.  Otherwise it will stay white.

Any black cell remains black  if the number of black neighbours is between N1 and N2. Otherwise it switches to white.

The Mobile Agent Model

A mobile-agents based model will look as follows. Agents are initially
dropped at one site of a two-dimensional lattice. Agents are black entitles moving through a white environment.

They move in discrete time and synchronously decide whether each one of them wants to move or prefer to stay.

An agent decides to leave its site if number of neighbourhood sites
occupied by agents does not belong to interval [N1, N2 ].

If agent decides to move then it jumps to one of neighbouring site, the agent prefers to select such sites such that the number of its occupied neighbours belongs to the interval [M1, M2 ].

Experiments

We vary N1, N2, M1 and M2.

Cellular Automata

We will develop cellular-automaton of 100×100 cells from initial random
configuration and snap configuration after 200 time steps.

You can run your own experiments here

http://uncomp.uwe.ac.uk/adamatzky/interdisciplinary/ga-ca/

Mobile agents

One thousand mobile agents will start their adventure at one site of 100×100 cell lattice, they will move and spread all over the lattice and positions of the agents will be fixed after thousand of steps (it takes longer for a population of mobile agents to reach some kind of stable or quasi-stable configuration comparing to cellular- automaton developments).

There are over thousand transition rules, plenty to choose from.

You can run your own experiments here

http://uncomp.uwe.ac.uk/adamatzky/interdisciplinary/mas/

Step 2: Aesthetic of Precipitation

To warm up we will enjoy a range of cellular-automaton configurations generated by the simplified rules of interval-based transitions, we assume that once cells become black ( take state 1)  the cell will remain in this state forever (like a precipitate in chemical reactions).

A catalog of cellular-automaton configurations for the precipitating
rule is shown in the figure below. In this figure, configurations of two-dimensional cellular automaton where cell state transition 0 → 1 happens only if the number of neighbours in state 1 belongs to the interval [M1, M2 ]. The automata started their evolution from random configuration and their configurations were recorded at time step 200. Each configuration is marked by values of M1and M2 used in transition rules to generate this configuration.

Step 3: Aesthetic of Association-Dissociation

The full spectrum of patterns generated by twiddling boundaries of [1, 2] and [1, 2] intervals is shown in http://uncomp.uwe.ac.uk/adamatzky/q2d1d2t1t2/ allconfs.pdf, where each configuration is marked by 4-digit sequence corre- sponding to 1212. During the workshop we will select most aesthetically appealing configuration and thus rules which generated them. 2 11 12 13 14 15 16 17 18 22 23 24 25 26 27 28 33 34 35 36 37 38 44 45 46 47 48 55 56 57 58 66 67 68 77 78 88 Figure 2: Configurations of two-dimensional cellular automaton where cell state transtion 0 ! 1 happens only if number of neighbours in state 1 belongs to the interval [1, 2]. The automata started their evolution from random configura- tion and their configurations were recorded at time step 200. Each configuration is marked by values of 1 and 2 used in transition rules to generate this con- figuration. 3 4 Step 4: Aesthetic and Computation We have several creteria to detect computational universality of cellular-automata, as well as any other dynamics system in physics, chemistry and biology, see (Adamatzky A. Computing in Nonlinear Media and Automata Collectives, IoP Publishing, 2001), is there any criterion of aesthetic? If computation emerges together with sexiness? Can beautiful be logically universal? Can ugly be functionally complete? We hope to find answers to these questions by the end of the Workshop. 4