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 fractalsSelf-similar intersectionsBox-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 generatorContour plotsGreedy graph coloringGraph6A few hundred interesting graphsThe Kings ProblemFirst order, autonomous systems of ODEsRunge-Kutta for systems of ODEs
Parametric Plot 2D
parametric_plot2d((u, v) => [2 * u + v, u - v], [0, 1], [0, 1])
parametric_plot2d(
(r, t) => [3 * r * Math.cos(t), r * Math.sin(t)],
[1, 2],
[Math.PI / 3, (5 * Math.PI) / 3],
{ width: 640, height: 400 }
)
function parametric_plot2d(f, [a, b], [c, d], opts = {}) {
let {
Nu = 100, // Total number of points the u domain is broken into
nu = 10, // Number of u gridlines
Nv = 100, // Total number of points the v domain is broken into
nv = 10, // Number of v gridlines
width = 800,
height = "auto",
pad = 20,
fill = d3.schemeCategory10[9],
fillOpacity = 1,
xticks = 5,
xtickValues,
xtickFormat,
xtickSize = 6,
yticks = 5,
ytickValues,
ytickFormat,
ytickSize = 6
} = opts;
let Du = (b - a) / Nu;
let Dv = (d - c) / Nv;
let u_cut = Math.floor(Nu / nu);
let v_cut = Math.floor(Nv / nv);
let data = [];
let k = 0;
let quads = [];
let lines = [];
let boundary = [];
for (let i = 0; i <= Nu; i++) {
for (let j = 0; j <= Nv; j++) {
let u = a + i * Du;
let v = c + j * Dv;
data.push(f(u, v));
if (i < Nu && j < Nv) {
quads.push([k, k + 1, k + Nv + 2, k + Nv + 1]);
}
if (j % v_cut == 0 && i < Nu) {
lines.push([k, k + Nv + 1]);
}
if (i % u_cut == 0 && j < Nv) {
lines.push([k, k + 1]);
}
if ((i == 0 || i == Nu) && j < Nv) {
boundary.push([k, k + 1]);
}
if ((j == 0 || j == Nv) && i < Nu) {
boundary.push([k, k + Nv + 1]);
}
k++;
}
}
let [xmin, xmax] = d3.extent(data.map((pt) => pt[0]));
let [ymin, ymax] = d3.extent(data.map((pt) => pt[1]));
if (height == "auto") {
height = ((ymax - ymin) * width) / (xmax - xmin);
}
xmin = xmin - 0.05 * (xmax - xmin);
xmax = xmax + 0.05 * (xmax - xmin);
ymin = ymin - 0.05 * (ymax - ymin);
ymax = ymax + 0.05 * (ymax - ymin);
let x_scale = d3
.scaleLinear()
.domain([xmin, xmax])
.range([pad, width - pad]);
let y_scale = d3
.scaleLinear()
.domain([ymin, ymax])
.range([height - pad, pad]);
let pts_to_path = d3
.line()
.x((d) => x_scale(d[0]))
.y((d) => y_scale(d[1]));
let svg = d3.create("svg").attr("width", width).attr("height", height);
let fill_group = svg.append("g").attr("fill", fill).attr("stroke", fill);
fill_group
.selectAll("polygon.fill")
.data(
quads.map(([i, j, k, l]) => [
x_scale(data[i][0]),
y_scale(data[i][1]),
x_scale(data[j][0]),
y_scale(data[j][1]),
x_scale(data[k][0]),
y_scale(data[k][1]),
x_scale(data[l][0]),
y_scale(data[l][1])
])
)
.join("polygon")
.attr("class", "fill")
.attr("points", (d) => d.toString())
.attr("opacity", fillOpacity);
let mesh = svg
.append("g")
.attr("stroke-width", 1)
.attr("stroke", "black")
.attr("opacity", 0.5);
mesh
.selectAll("line.mesh")
.data(
lines.map(([i, j]) => ({
x1: x_scale(data[i][0]),
x2: x_scale(data[j][0]),
y1: y_scale(data[i][1]),
y2: y_scale(data[j][1])
}))
)
.join("line")
.attr("class", "mesh")
.attr("x1", (d) => d.x1)
.attr("x2", (d) => d.x2)
.attr("y1", (d) => d.y1)
.attr("y2", (d) => d.y2);
let bounds = svg
.append("g")
.attr("stroke", "black")
.attr("stroke-width", 5)
.attr("class", "boundary")
.selectAll("line.boundary")
.data(
boundary.map(([i, j]) => ({
x1: x_scale(data[i][0]),
x2: x_scale(data[j][0]),
y1: y_scale(data[i][1]),
y2: y_scale(data[j][1])
}))
)
.join("line")
.attr("class", "boundary")
.attr("x1", (d) => d.x1)
.attr("x2", (d) => d.x2)
.attr("y1", (d) => d.y1)
.attr("y2", (d) => d.y2);
////////
// The axes
let xAxisPosition;
if (ymin <= 0 && 0 <= ymax) {
xAxisPosition = y_scale(0);
} else {
xAxisPosition = height - pad;
}
let yAxisPosition;
if (xmin <= 0 && 0 <= xmax) {
yAxisPosition = x_scale(0);
} else {
yAxisPosition = pad;
}
svg
.append("g")
.style("font-size", "16px")
.attr("transform", `translate(0, ${xAxisPosition})`)
.call(
d3
.axisBottom(x_scale)
.ticks(xticks)
.tickValues(xtickValues)
.tickFormat(xtickFormat)
.tickSize(xtickSize)
.tickSizeOuter(0)
);
svg
.append("g")
.attr("id", "y-axis")
.style("font-size", "16px")
.attr("transform", `translate(${yAxisPosition})`)
.call(
d3
.axisLeft(y_scale)
.ticks(yticks)
.tickValues(ytickValues)
.tickFormat(ytickFormat)
.tickSize(ytickSize)
.tickSizeOuter(0)
);
return svg.node();
}
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.