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This is a badly titled question...maybe a moderator can make it better.

Nearly two decades ago, I took a computer graphics class as an undergraduate. We got to do whatever we wanted for a final project as long as it demonstrated what we learned about CG.

So, I read a book (I can't think of the name at all) that described a methodology to generate fractal images starting with a simple shape and mutating it using substitution. It described abstract fractals and tree/flower fractals. I do recall implementing the Sierpinski Triangle in one of my sample imputs as well as a 3D tree.

The input to the program was basically a series of arbitrary symbols defined by the program. -----= might represent a rose. Then you apply some substitutions for a given pattern. --= > -+=---= might represent a longer rose with thorns. So, applying that pattern to the initial string you get ----+=---=. Finally you loop over this string N number of times to create some desired effect.

The book itself offered a ton of inputs with sample pictures, but no actual source code. The implementation was completely left up to the developer.

I would like to know if somebody can help me with the terminology for this technique and bonus points for the name of the book (or a book) that described this process?

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  • Perhaps you're thinking of term rewriting? Commented Aug 26, 2014 at 19:23

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My first guess is that you're thinking of L-systems: http://en.m.wikipedia.org/wiki/Lindenmayer_system

I found this example at http://en.m.wikipedia.org/wiki/Koch_snowflake , linked from the Sierpinski page:

The Koch Curve can be expressed by a rewrite system (Lindenmayer system). Alphabet : F Constants : +, − Axiom : F++F++F Production rules: F → F−F++F−F Here, F means "draw forward", + means "turn right 60°", and − means "turn left 60°".
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  • That's it exactly! +1000 if I could! Commented Aug 26, 2014 at 19:49
  • Here's a link to the book that I used: algorithmicbotany.org/papers/#abop Commented Aug 26, 2014 at 20:01
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What the program is most likely doing is taking the input pattern and interpreting each symbol as a "command", which are run in a looping sequence as modifications to a basic drawing pattern. For instance, "-" might be "draw the next line segment normally". "=" might be "draw this line segment thicker than normal", ">" might be "turn left" and "<" would be "turn right", and finally "+" could mean "start drawing in three directions in parallel".

So, it's basically just a command parsing algorithm. A relatively novel one, but on the whole no more complex than something written to parse more verbose commands.

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