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.
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 examplesMcMullen carpetsSelf-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
The Twindragon (with boundary)
// Note that the matrix AInv, the digit set D,
// and the set of shifts F are defined below.
digraphIFS = {
let edges = [];
let eps = 0.00000001;
for (let i = 0; i < F.length; i++) {
for (let j = 0; j < F.length; j++) {
D.forEach(function (d) {
D.forEach(function (dp) {
let alpha = F[i];
let beta = F[j];
let Aalpha = math.multiply(A, alpha);
let x = Aalpha[0] + dp[0] - d[0];
let y = Aalpha[1] + dp[1] - d[1];
if (math.abs(x - beta[0]) < eps && math.abs(y - beta[1]) < eps) {
edges.push({
source: i,
target: j,
f: new AffineFunction([AInv, math.multiply(AInv, d)])
});
}
});
});
}
}
return new DigraphIFS(edges);
}
digraphIFS.dimension
digraphIFS.show_digraph()
digraphIFS.render_stochastic({
image_width: width < 500 ? width : 500,
n: 100000,
colors: true,
color_depth: 4
})[6]
f_invs = fs.map((af) => af.invert())
IFS = new IteratedFunctionSystem(fs)
F = [
[1, 0],
[1, 1],
[0, 1],
[-1, 0],
[-1, -1],
[0, -1]
]
fs = D.map((d) => new AffineFunction([AInv, math.multiply(AInv, d)]))
D = [
[0, 0],
[1, 0]
]
AInv = math.inv(A)
A = [
[1, 1],
[-1, 1]
]
// Used for pre-generated images:
//
// attractor = IFS.deterministic_path_approximation({
// init: [
// [0, 0],
// [1, -1],
// [2, 0],
// [1, 1]
// ],
// max_depth: 15
// }).flat(1)
import {
IteratedFunctionSystem,
AffineFunction,
shift,
scale,
rotate,
degree
} from "@mcmcclur/iteratedfunctionsystem-class"
import { DigraphIFS } from "@mcmcclur/digraphifs-class"
math = require("mathjs")
Purpose-built for displays of data
Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
