I'm a professor of mathematics at the University of North Carolina Asheville. I've also done a fair amount of consulting work over the years focusing on scientific and data visualization.
I'm happy to be part of the first Observable Ambassador's cohort.
Public
Edited
Dec 31, 2023
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1 star
IFS QuickstartIterated Function SystemsConstruction of the Serpinski triangleThe Sierpinski pedal triangleSimilarity and the Pedal TriangleDeterministic IFS algorithmsSelf-similar spiralsStochastic IFS algorithmsGeneralized Sierpinski trianglesThe Z-CurvePoly-gasketsThe Koch snowflakeBarnsley's fernIteratedFunctionSystem ClassAffineFunction ClassSimilarity transformationsThe TwindragonBox-counting dimension examplesThe Twindragon (with boundary)Self-affine tilesTutorial on self-affine tilesA self-affine tile with holesSelf-affine tiles via polygon mergeThe Eisenstein fractionsGolden rectangle fractalsDeterministic digraph IFS algorithmsA stochastic digraph IFS algorithmMixed self-similarityFractalized squareHilbert's coordinate functionsRauzy Fractals
McMullen carpets
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Math
{
// Note how the 0-1 pattern in the matrix below specifies
// which sub-rectangles are on or off in the image.
let M = [
[0, 1, 1],
[1, 0, 0],
[0, 1, 0],
[0, 1, 1]
];
// The rest should be automatic.
let m = M[0].length;
let n = M.length;
let A = [
[1 / m, 0],
[0, 1 / n]
];
let IFS = [];
for (let i = 1; i <= m; i++) {
for (let j = 1; j <= n; j++) {
if (M[j - 1][i - 1]) {
IFS.push([A, [(i - 1) / m, 1 - j / n]]);
}
}
}
return new IteratedFunctionSystem(IFS).render_stochastic({
n: 60000,
colors: true,
axes: true,
extent: [
[-0.05, 1.05],
[-0.05, 1.05]
],
image_width: width < 900 ? width : 900
});
}
exampleIFS = {
let m = mn.m;
let n = mn.n;
let A = [
[1 / m, 0],
[0, 1 / n]
];
let ifs = [];
let M = 0;
let N = 0;
while (N == 0) {
for (let i = 0; i < m; i++) {
let Mi = 0;
for (let j = 0; j < n; j++) {
if (d3.randomUniform()() < mn.c) {
N = N + 1;
Mi = Mi + 1;
ifs.push([A, [i / m, j / n]]);
}
}
M = M + Math.sign(Mi);
}
}
mn.M = M;
mn.N = N;
return new IteratedFunctionSystem(ifs);
}
mn = {
redo;
let c = d3.randomUniform(0.1, 1)();
let m = d3.randomInt(2, 5)();
let n = d3.randomInt(m + 1, 7)();
return { c: c, m: m, n: n };
}
import { IteratedFunctionSystem } from "@mcmcclur/iterated-function-systems"
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