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.
A Julia set on the Riemann sphereThe Z-CurveBarnsley's fernA stochastic digraph IFS algorithmSelf-affine tilesThe TwindragonThe Eisenstein fractionsA self-affine tile with holesSelf-affine tiles via polygon mergeGolden rectangle fractalsBifurcation diagram with critical curvesThe tame twindragonIllustrations for the proof of Green's theoremNon-orientability of a Mobius stripExamples of parametric surfacesPenrose tilingThe extended unit circlePenrose three coloringNewtons's method on the Riemann sphereConic sectionsDivisor graphsThe dance of Earth and VenusIterating multiples of the sine functionBorderline fractalsBox-counting dimension examplesMandelbrot by dimensionInverse iteration for quadratic Julia setsInteger Apollonian PackingsIllustrations of two-dimensonal heat flowThe logistic bifurcation locusThe eleven unfoldings of the cubeA unimodal function with fractal level curvesGreen's theorem and polygonal areaThe geometry and numerics of first order ODEsThe xxx^xxx-spindleAnimated beatsRauzy FractalsHilbert's coordinate functionsPluckNot PiDrum strikeThe Koch snowflakeFractalized squareA Taylor series about π/4\pi/4π/4PlotX3D HyperboloidA PlotX3D animationModular arithmetic in 5th grade artSimple S-I-R ModelThe Poisson KernelPoly-gasketsClassification of 2D linear systems via trace and determinantJulia sets and the Mandelbrot setWater wavesFourier SeriesDisks for a solid of revolutionOrbit detection for the Mandelbrot setTracing a path on a spherePlot for mathematiciansFunctions of two variablesPartial derivativesDijkstra's algorithm on an RGGGradient ascentUnfolding polyhedraTangent plane to a level surfaceA strange discontinuityExamples of level surfacesMcMullen carpetsHills and valleysThe definition of ⇒Double and iterated integralsMST in an RGGTrees are bipartiteFractal typesettingd3.hierarchy and d3.treeK23 is PlanarPolar CoordinatesParametric region generatorParametric Plot 2DContour plotsGreedy graph coloringGraph6A few hundred interesting graphsThe Kings ProblemFirst order, autonomous systems of ODEsRunge-Kutta for systems of ODEs
Self-similar intersections
// The digraph IFS that arises from application
// of the algorithm described in the paper.
digraphIFS = {
let g = transform.g;
let fs = IFS.IFS.affine_function_list;
let f_invs = fs.map((af) => af.invert());
let pts = fs.map((af) => af.fixed_point);
let P0 = new Flatten.Polygon(pts.map((xy) => Flatten.point(xy)));
let C = [g];
let S = [g];
// for (let i = 0; i < 8; i++) {
while (S.length > 0) {
S = step1(S).filter(test);
let test2 = (f) => C.map((F) => F.equal(f)).indexOf(true) > -1;
S = S.filter((f) => !test2(f));
let S_new = [];
S.forEach(function (f) {
let is_in = S_new.map((F) => f.equal(F)).indexOf(true) > -1;
if (!is_in) {
S_new.push(f);
}
});
S = S_new;
C = C.concat(S);
}
let edges = [];
for (let i = 0; i < C.length; i++) {
for (let j = 0; j < C.length; j++) {
fs.forEach(function (fi, k) {
fs.forEach(function (fj) {
let g = C[i];
let h = C[j];
let fi_inv = f_invs[k];
if (fi_inv.compose(g).compose(fj).equal(h)) {
edges.push({
source: i,
target: j,
f: fi
});
}
});
});
}
}
let digraphIFS = new DigraphIFS(edges);
digraphIFS.C = C;
return digraphIFS;
function test(af) {
let P = new Flatten.Polygon(pts.map((xy) => Flatten.point(af.f(xy))));
return P0.intersect(P).length > 0;
}
function step1(S) {
return f_invs
.map((F) => S.map((g) => fs.map((f) => F.compose(g).compose(f))))
.flat(2);
}
}
import { DigraphIFS } from "@mcmcclur/digraphifs-class"
import {
AffineFunction,
IteratedFunctionSystem,
scale,
rotate,
shift,
reflect,
degree
} from "@mcmcclur/iteratedfunctionsystem-class"
// Computational geometry library used to detect overlap
// between the image of a convex set and itself.
Flatten = require("@flatten-js/core")
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.
