30:Taa9,## More info This notebook is one of a series of notebooks that implement, document, and provide examples to illustrate how to use the `IteratedFunctionSystem` class to generate and analyze self-similar sets. Other notebooks in the series include: * [Iterated Function Systems](https://observablehq.com/@mcmcclur/iterated-function-systems)
The longest notebook in the series that contains a few more basic examples and documentation of all the properties and methods of the `IteratedFunctionSystem` class * [Construction of the Sierpinski triangle](https://observablehq.com/@mcmcclur/construction-of-the-serpinski-triangle)
A discussion of one of the most fundamental self-similar sets * [Sierpinski pedal triangles](https://observablehq.com/@mcmcclur/the-sierpinski-pedal-triangle)
A variation of the Sierpinski triangle that's a bit more challenging to understand * [Similarity and the pedal triangle](https://observablehq.com/@mcmcclur/similarity-and-the-pedal-triangle)
An explanation of why the Sierpinski pedal triangle is even a self-similar set at all. * [Deterministic algorithms](https://observablehq.com/@mcmcclur/deterministic-ifs-algorithms)
A discussion of deterministic algorithms for generating self-similar sets with a specific emphasis on tackling the difficulties that arise in the construction of the Sierpinski pedal triangle * [Self-similar spirals](https://observablehq.com/@mcmcclur/self-similar-spirals)
A beautiful class of self-similar sets that require some analysis to generate * [Stochastic algorithms](https://observablehq.com/@mcmcclur/stochastic-ifs-algorithms)
discussion of stochastic algorithms for generating self-similar sets with a specific emphasis on tackling the difficulties that arise in the generation of self-similar spirals * More examples * [Generalized Sierpinski triangles](https://observablehq.com/@mcmcclur/generalized-sierpinski-triangles) * [The Z-Curve](https://observablehq.com/@mcmcclur/the-z-curve) * [Poly-gaskets](https://observablehq.com/@mcmcclur/poly-gaskets) * [The Koch snowflake](https://observablehq.com/@mcmcclur/the-koch-snowflake) * [Barnsley's fern](https://observablehq.com/@mcmcclur/barnsleys-fern) * [The `IteratedFunctionSystem` class](https://observablehq.com/@mcmcclur/iteratedfunctionsystem-class)
Implementation * [The `AffineFunction` class](https://observablehq.com/@mcmcclur/affinefunction-class)
More implementation * [Similarity transformations](https://observablehq.com/@mcmcclur/similarity-transformations)
A discussion of similarity transformations, which `IteratedFunctionSystem`s for self-similar sets are built upon. 31:[] 2e:{"title":"IFS Quickstart","cells":[{"id":0,"value":"# IFS Quickstart\n\nJust a minimal working example intended to illustrate how easy it is to get started with [IteratedFunctionSystems](https://observablehq.com/@mcmcclur/iterated-function-systems).","pinned":false,"hidden":false,"mode":"md"},{"id":47,"value":"// Define an IFS\nIFS = new IteratedFunctionSystem([\n scale(0.5),\n scale(0.5, [1, 0]),\n scale(0.5, [0, 1])\n])","pinned":true,"hidden":false,"mode":"ojs"},{"id":39,"value":"// The easiest way to visualize is with IFS.render_stochastic\nIFS.render_stochastic({ colors: true })","pinned":true,"hidden":false,"mode":"ojs"},{"id":42,"value":"// IFS.render_deterministic is another option\nIFS.render_deterministic({\n max_depth: 4,\n init: [\n [0, 0],\n [1, 0],\n [0, 1]\n ],\n fill_colors: true\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":5,"value":"// All built on top of the following imports\nimport {\n IteratedFunctionSystem,\n scale,\n shift,\n rotate,\n reflect,\n pi,\n degree\n} from \"@mcmcclur/iteratedfunctionsystem-class\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":14,"value":"$30","pinned":false,"hidden":false,"mode":"md"}],"files":"$W31","stdlib":"1","titling":"auto"}