Nested Tiles
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Yesterday, I was inspired by skimming through Stephen Wolfram's book A New
Kind of Science. He wrote about
cellular automata,
and I thought of another type of system in the genre of
tiles-with-rules that I am calling nested tiles
. It's a way of
generating an image like a context-free grammar is a way of generating text.
Alternative names for this concept could be
- color pattern substitution,
- color pattern rewriting,
- color pattern replacement,
- image pattern substitution,
- image rewriting,
- image pattern substitution,
- tile pattern replacement,
- tile rewriting,
- or tile pattern substitution;
and you could stick the word context-free
in front and/or stick either of the words system
or grammar
at the end.
A nested tiles system
consists of a set of rules.
Each rule has a type/color of cell that it applies to and a rectangle of cells that the cell is replaced with.
The nested tiles process is applied to an initial image and produces a new image according to the rules.
In this way, the next step of applying the rules for each tile is independent of any other tile.
My simplest example is for a ruleset where each tile is substituted with a 2x2 rectangle,
which implies that the image size grows with each step.
In my implementation, if a multiple rules apply to a tile, one of the rules is chosen at random.
Example nested tile rule:
Gallery of nested tile results:
(click on images to see full details)
Each of the previous images in the gallery started with the initial state of a single 1x1 image.
At the moment, I haven't heard of a image system like this, so if you know about one, please let me know. I think that this is a nice technique for making generative art. I plan on making a dedicated nested tiles page soon!
I plan on more updates to come