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.
Frank implemented this brilliantly. This makes it so much easier and quicker to find new interesting patterns. Thank you Frank.
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.
A couple of things to note – images wrap left and right and are in fact, negatives (pixels white out of black).
Below are few examples, of where I have started with a small group of pentagons and continued (by repetition) to arrange them in a line, then working outward, both left and right. The question is, can the ‘spine’ be forced to reappear somewhere else (along the horizontal axis) as the pattern expands?
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.
Below is another larger motif I made up. It can also be interspersed with modules.
A special thank you to Jaap Scherphuis for his invaluable input and to David Bailey for helping early on.
Three really nice examples of (glide) mirror symmetry using the same pentagon, courtesy of Jaap Sherphuis. The only thing I did was recolour them.
This large motif was kindly sent in by Jaap Scherphuis. It consists of 28 pentagons and can be tiled in two ways.
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.
Here’s a few more by me…
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).
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.
Module 2 & 4 produce this…
By adding module 3 to the above, a familiar pattern emerges (but in strips).
By combining all modules, anything can happen!