[CA Wallpaper] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

Pages:1


CA Wallpaper

(Click here to view the original thread with full colors/images)


Posted by: Jason Cawley

By Jason Cawley and Richard Phillips, Wolfram Research


One can create a huge variety of interesting repetitive patterns using multicolored Cellular Automata, suitable for "wallpaper" of the computer desktop or the physical variety, or for use as fabric designs etc.

The scheme used here is to give a 1D CA a periodic initial condition and then to trim off any leading transient, giving a purely periodic pattern. As the size of the repetitve "seed" is changed, one gets larger repeating elements that "tile" the plane in different ways. The variety of these is set by all possible combinations of initial condition "seeds" of that width. One can also enumerate simple colors schemes, as selections of a few colors out of a modest set or "palette". And of course, there is a huge space of CA rules to which this scheme may be applied. As a result, one can readily construct a repetitive pattern space in which a tuple of integers specifies a particular pattern, and every combination yields a different design, many of them quite striking aesthetically. One can explore the resulting space systematically or randomly. The scheme can readily be generalized to more colors per design or to a revised or larger color palette.

The attached notebook shows how this works, with all the code necessary and some examples. I will attach a zip of bitmap of examples below, for those without Mathematica.

You can use these on your desktop in Windows by saving the bmp to your pictures folder, then right-click anywhere on your desktop and selecting "properties" from the pop-up menu. Select the "desktop" tab. Then "browse" to the image, or select it in the window on the left. Then set the "position" setting on the right to "tile", and hit "apply".

If you want a single instance of the pattern to cover your desktop without using the "tile" feature in Windows, you can modify the ArrayPlot function calls in the attached notebook with e.g. ImageSize->1200. Right-click on the image in your Mathematica, and choose "Copy As..." then "Bitmap". Open Paint and "paste" in the image, touch up borders if you like, and save the file to your images folder to show it to Windows as a potential desktop.

I hope this is fun.


Posted by: Jason Cawley

Here is a zip of 12 sample CA Wallpapers, desktop size.




Forum Sponsored by Wolfram Research

© 2004-2008 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. | Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings