The Sierpinski pedal triangle / Mark McClure

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.

Workspace

Published

Fractals

Edited

Oct 18, 2021

Importers

2 stars

IFS = pedalIFS(...vertices)

vertices = [

[0, 0],

[1, 0],

[0.4, 0.6]

]

function pedalIFS(A, B, C) {

let a = Math.sqrt((B[0] - C[0]) ** 2 + (B[1] - C[1]) ** 2);

let b = Math.sqrt((A[0] - C[0]) ** 2 + (A[1] - C[1]) ** 2);

let c = Math.sqrt((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2);

let alpha = (b ** 2 + c ** 2 - a ** 2) / (2 * b * c);

let beta = (a ** 2 + c ** 2 - b ** 2) / (2 * a * c);

let gamma = (a ** 2 + b ** 2 - c ** 2) / (2 * a * b);

if (alpha > 0 && beta > 0 && gamma > 0) {

let AB = [B[0] - A[0], B[1] - A[1]];

let AC = [C[0] - A[0], C[1] - A[1]];

let fa = scale(alpha, A).compose(flip(AB, AC, A));

let BA = [A[0] - B[0], A[1] - B[1]];

let BC = [C[0] - B[0], C[1] - B[1]];

let fb = scale(beta, B).compose(flip(BA, BC, B));

let CA = [A[0] - C[0], A[1] - C[1]];

let CB = [B[0] - C[0], B[1] - C[1]];

let fc = scale(gamma, C).compose(flip(CA, CB, C));

return new IteratedFunctionSystem([fa, fb, fc]);

} else {

throw "Non accute triangle";

}

// Suppose two vectors u and v emanate from the point o.

// This function returns the reflection about the line through

// the point o that bisects the angle made by u and v, essentially

// flipping the positions of u and v, though not their magnitudes.

function flip(u, v, o = [0, 0]) {

let [ux, uy] = u;

let [vx, vy] = v;

let normu = Math.sqrt(ux ** 2 + uy ** 2);

ux = ux / normu;

uy = uy / normu;

let normv = Math.sqrt(vx ** 2 + vy ** 2);

vx = vx / normv;

vy = vy / normv;

let bisector = [ux + vx, uy + vy];

let n = [-bisector[1], bisector[0]];

return reflect(n, o);

}

import { scale, reflect } from "@mcmcclur/affinefunction-class"

import { IteratedFunctionSystem } from "@mcmcclur/iteratedfunctionsystem-class"

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.

Learn more