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.
// 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")
One platform to build and deploy the best data apps
Experiment and prototype by building visualizations in live JavaScript notebooks. Collaborate with your team and decide which concepts to build out.
Use Observable Framework to build data apps locally. Use data loaders to build in any language or library, including Python, SQL, and R.
Seamlessly deploy to Observable. Test before you ship, use automatic deploy-on-commit, and ensure your projects are always up-to-date.