Shape of things…

These images have come about, after I sent an email to Frank Buss (who I had never heard of previously) as I knew he had an interest in 1D cellular automata.

In no time (and to my surprise) he sent me a link to a program he had put together in Javascript to create 16 random rules at a time. I then asked if it were possible to adapt the software to include a variation button.

Frank implemented this brilliantly. This makes it so much easier and quicker to find new interesting patterns.  Thank you Frank.

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1D Life Pattern Rules OK

I have been using Mirek Wójtowicz’s brilliant Mcell program, on and off for many a year now, creating hundreds of life patterns in the process.  Below is a random selection of the more interesting (and often surprising) ones I have discovered.

w168-2

w69

v132a

c72b

c73e

c126a

c102a

mcell-c147a

mcell-c112

c68

v41

A couple of things to note – images wrap left and right and are in fact, negatives (pixels white out of black).

Pulse tiling

This was my attempt at a radial tiling.  I ended up with a curious ‘pulse’ or ‘shift’ in the pattern, causing a ripple effect, that can only repeat along one axis.  This is yet be fully understood.
ds-tiling5
 Below is another larger motif I made up.  It can also be interspersed with modules.

ds-tiling4ds-tiling4a

A special thank you to Jaap Scherphuis for his invaluable input and to David Bailey for helping early on.

More Pentagon motifs

This large motif was kindly sent in by Jaap Scherphuis.  It consists of 28 pentagons and can be tiled in two ways.

jaaptiling1a

By omitting the module far right (highlighted in dark red) a slightly smaller motif emerges which can tile in a few ways.  One example shown below.

jaaptiling1b

Here’s a few more by me…

ds-tiling9

ds-tiliing1c

ds-tiling9a

The last one is interesting as I have implemented mirroring rather than rotation.  Also, by spinning this motif through 180° and combining with the original, tilings of an aperiodic nature can develop (example to follow).

Pentagon modules

This pentagon continues to surprise me.  By joining three or more of these shapes together, modules are formed.  The four below can be combined in a number of ways to produce large motifs.

modules

Module 2 & 4 produce this…

modulesex1

By adding module 3 to the above, a familiar pattern emerges (but in strips).

modulesex2a

 

By combining all modules, anything can happen!

ModulesEx2b.jpg