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 carpetsThe Twindragon (with boundary)Self-affine tilesTutorial on self-affine tilesA self-affine tile with holesSelf-affine tiles via polygon mergeThe Eisenstein fractionsGolden rectangle fractalsA stochastic digraph IFS algorithmMixed self-similarityFractalized squareHilbert's coordinate functionsRauzy Fractals
Deterministic digraph IFS algorithms
Also listed in…
Digraph Fractals
p = (1 + Math.sqrt(5)) / 2
full_digraph_input = [
{
// Rectangle in rectangle
source: "R",
target: "R",
f: shift([p, 0])
.compose(rotate(pi / 2))
.compose(scale(1 / p)),
label: "RR"
},
{
// Square in rectangle - don't delete!!
source: "R",
target: "S",
f: scale(1),
label: "RS"
},
{
// Lower left rectangle in square
source: "S",
target: "R",
f: scale(1 / p ** 2),
label: "SR1"
},
{
// Lower right rectangle in square
source: "S",
target: "R",
f: shift([1 / p + 1 / p ** 2, 0])
.compose(scale(1 / p ** 2))
.compose(rotate(pi / 2)),
label: "SR2"
},
{
// Upper left rectangle in square
source: "S",
target: "R",
f: shift([0, 1])
.compose(scale(1 / p ** 2))
.compose(rotate((3 * pi) / 2)),
label: "SR3"
},
{
// Upper right rectangle in square
source: "S",
target: "R",
f: shift([1, 1])
.compose(scale(1 / p ** 2))
.compose(rotate(pi)),
label: "SR4"
},
{
// Square in square
source: "S",
target: "S",
f: shift([1 / p ** 2, 1 / p ** 2]).compose(scale(1 / p ** 3)),
label: "SS"
}
]
full_digraphIFS = new DigraphIFS(full_digraph_input)
// Good initiators for the deterministic method
init = [
[
[0, 0],
[p, 0],
[p, 1],
[0, 1],
[0, 0]
],
[
[0, 0],
[1, 0],
[1, 1],
[0, 1],
[0, 0]
]
]
full_digraphIFS.render_deterministic("S", {
initiators: init,
max_depth: 3,
color_depth: 3,
colors: ["lightgray", "#D11E00"],
stroke: true
})
{
let clone = full_digraph_input.map((o) => Object.assign({}, o));
clone.splice(5, 1);
return new DigraphIFS(clone).render_deterministic("R", {
max_depth: 7,
initiators: init,
colors: false
});
}
{
let clone = full_digraph_input.map((o) => Object.assign({}, o));
clone.splice(5, 1);
return new DigraphIFS(clone).render_deterministic("R", {
max_depth: Infinity,
tolerance: 0.005,
initiators: init,
colors: false
});
}
import {
scale,
shift,
rotate,
reflect,
pi,
DigraphIFS
} from "@mcmcclur/digraphifs-class"
MathJax = require("https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js").catch(
() => window["MathJax"]
)
Purpose-built for displays of data
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