This repository contains code to render L-systems with different polar shapes. You can play with the pattern generator here. You can view examples of patterns I have created here. You can find example sketches here. It is also here.
From Wikipedia:
"An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures."
If you want to learn more about using L-systems to generate fractals, I highly recommend Daniel Shiffman's Fractal Trees L-system Coding Challenge. I have used the L-system formulas by Paul Bourke to generate these designs. The rulesets can be found in the ruleset.json file. The code for the shapes is pulled from a couple of different sources: The Coding Train, Mathcurve.com, and Wolfram Mathworld
I have experimented with inserting different shapes--including gears, spirals, ovals, and even the supershape--into different L-system rule-sets. It is hard to predict, in advance, whether a particular rule-set/shape combination is going to produce a nice design, but trial and error have resulted in some pretty cool patterns. The current version of the sketch will render two different rule-sets. Here is a link to the latest version of my p5-sketch.
Daniel Shiffman recently recleased a Coding Challenge on the dragon fractal, and my experiments started with the Dragon rule-set. One of my favorites is this image, which was created using two dragon fractals filled with the gear curve (level 12).
Since many of the shapes are a function of parameters that can be altered, I added sliders to experiment with different rule-set/shape curve combinations. Sometimes when you insert a shape into a rule-set, the result is quite different from the typical visualization. One example is inserting the cassini curve into the Hilbert rule-set. I am not sure that many people would look at this image and realize how it was generated.
I have discovered that both the Hilbert and Peano curve rule-sets can be used to generate some nice backgrounds. Here is the Hilbert curve rule-set rendered with the gear curve (purple background) and the ADH23a ruleset with bicorn shape:
Why stop with just one ruleset or shape? Here I have rendered the ADH231a ruleset twice with the flower and supershape curves.
Of course, one of the original applications for L-systems is creating realistic looking trees. I think adding a shape to the rule-set can improve the look of the trees. For example, here is a tree rendered with the zig-zag curve.
I also want to give a shout-out to supercolorpalette.com! I started out by creating a json file with palettes, but eventually found the supercolorpalette website. I was able to get the HEX codes from the url, and then create palette arrays very easily with some helper functions from chatGPT -- so much easier and faster than manually creating the palette arrays.