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.
Published
Edited
Dec 6, 2021
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 examplesMcMullen carpetsThe Twindragon (with boundary)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
Tutorial on self-affine tiles
Also listed in…
Fractal tiling
// You can edit this to generate your own tile.
A = [
[2, -2],
[2, 0]
]
IFS = {
let AInv = math.inv(A);
return new IteratedFunctionSystem(
base_digit_set(A).map(
(d) => new AffineFunction([AInv, d]) // math.multiply(AInv, d)
)
);
}
basic_picture = IFS
// .iterate(3) // Uncomment this to generate a higher order tiling
.render_stochastic({
n: 200000,
colors: true,
image_width: width < 800 ? width : 800
})
base_digit_set(A)
digit_pic(A)
D = [
[0, 0],
[1, 1],
[-1, 0],
[0, -1]
]
differentD = {
let AInv = math.inv(A);
return (
new IteratedFunctionSystem(D.map((d) => new AffineFunction([AInv, d])))
//.iterate(3) // Uncomment this to generate a higher order tiling
.render_stochastic({
n: 200000,
colors: true,
image_width: width < 800 ? width : 800
})
);
}
different_basis = {
let S = [
[1, -1 / 2],
[0, math.sqrt(3) / 2]
];
let SAInvSInv = math.multiply(S, math.inv(A), math.inv(S));
return (
new IteratedFunctionSystem(
D.map((d) => new AffineFunction([SAInvSInv, math.multiply(S, d)]))
)
//.iterate(3) // Uncomment this to generate a higher order tiling
.render_stochastic({
n: 200000,
colors: true,
image_width: width < 800 ? width : 800
})
);
}
evd = new mlm.EigenvalueDecomposition(A)
is_expansive = evd.d[0] ** 2 + evd.e[0] ** 2 > 1 &&
evd.d[1] ** 2 + evd.e[1] ** 2 > 1
det = A[0][0] * A[1][1] - A[0][1] * A[1][0]
import { base_digit_set, digit_pic } from "@mcmcclur/self-affine-tiles"
import {
AffineFunction,
IteratedFunctionSystem,
shift,
rotate,
degree,
pi
} from "@mcmcclur/iteratedfunctionsystem-class"
mlm = require("ml-matrix")
math = require("mathjs")
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