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
Oct 10, 2021
5 stars
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 snowflakeIteratedFunctionSystem 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 fractalsDeterministic digraph IFS algorithmsA stochastic digraph IFS algorithmMixed self-similarityFractalized squareHilbert's coordinate functionsRauzy Fractals
Barnsley's fern
Also listed in…
Math
barnsleyIFS = {
let IFS = new IteratedFunctionSystem([
[
[
[0.85, 0.04],
[-0.04, 0.85]
],
[0, 1.6]
],
[
[
[-0.15, 0.28],
[0.26, 0.24]
],
[0, 0.44]
],
[
[
[0.2, -0.26],
[0.23, 0.22]
],
[0, 1.6]
],
[
[
[0, 0],
[0, 0.16]
],
[0, 0]
]
]);
return IFS;
}
barnsleyIFS.render_deterministic({
init: outline,
image_width: width,
image_height: 800,
extent: [[-2.2, 2.7], [0, 9.6]],
tolerance: tolerance,
max_depth: Infinity,
fill_colors: ["#008800", "#00aa00", "#00aa00", "#000000"],
stroke_colors: ["#002200", "#004400", "#004400", "#000000"]
//axes: { origin: [-2.5, -0.2], font: "16px Times" }
})
{
let canvas = barnsleyIFS.render_deterministic({
init: outline,
image_width: width,
image_height: 800,
tolerance: 0,
max_depth: 1,
fill_colors: ["#008800", "#00aa00", "#00aa00", "#000000"],
stroke_colors: ["#002200", "#004400", "#004400", "#000000"],
axes: { origin: [-2.5, -0.2], font: "16px Times" }
});
let x = barnsleyIFS.xScale;
let y = barnsleyIFS.yScale;
let ctx = canvas.getContext("2d");
ctx.beginPath();
ctx.moveTo(x(outline[0][0]), y(outline[0][1]));
ctx.strokeStyle = "black"; // 'rgba(0,0,0,0.5)';
ctx.lineWidth = 3;
for (let j = 0; j < outline.length; j++) {
ctx.lineTo(x(outline[j][0]), y(outline[j][1]));
}
ctx.lineTo(x(outline[0][0]), y(outline[0][1]));
ctx.stroke();
ctx.closePath();
return canvas;
}
outline = {
let [f1, f2, f3, f4] = barnsleyIFS.function_list;
let tip = [0, 0];
for (let i = 0; i < 100; i++) {
tip = f1(tip);
}
let xy = f2(tip);
let left_side = [xy].concat(d3.range(32).map(() => (xy = f1(xy))));
left_side.reverse();
xy = f3(tip);
let right_side = [xy].concat(d3.range(32).map(() => (xy = f1(xy))));
let outline = [[0, 0]].concat(right_side).concat([tip]).concat(left_side);
return outline;
}
import { IteratedFunctionSystem } from "@mcmcclur/iteratedfunctionsystem-class"
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