Mandelbrot using the Contour Lines utility from Reinder:
Metaball Contour Lines
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// LL 2021 const turtle = new Turtle(); const detail_z = 8; // min=1, max=10, step=1 const detail_xy = 0.5; // min=0.01, max=1, step=0.01 const max_iterations = 25 // min = 1, max = 100, step = 1 const m_scale = 80 // min = 10, max = 1000, step = 0.01 const offset_x = 0.73 // min = -10, max = 10, step = 0.001 const offset_y = 0 // min = -10, max = 10, step = 0.001 function mandelbrot(x, y) { var cr = x var ci = y var zr = 0 var zi = 0 var iterations = 0 while (zr * zr + zi * zi < 4) { const new_zr = zr * zr - zi * zi + cr const new_zi = 2 * zr * zi + ci zr = new_zr zi = new_zi iterations += 1 if (iterations >= max_iterations) break } return iterations //var l = Math.sqrt(zr * zr + zi * zi) //return iterations + 1. - Math.log(Math.log2(l)) //return (iterations == max_iterations) ? max_iterations : 0 } function zFunc(p) { //return ((Math.sin(p[0]/10) + Math.cos(p[1]/10)) / 4 + 0.5) * (detail_z+1); const m_x = p[0] / m_scale - offset_x; const m_y = p[1] / m_scale - offset_y; const m = mandelbrot(m_x, m_y) / max_iterations; return m * (detail_z+1); } function walk(i) { const lines = ContourLines(i, (1/detail_xy)/(1+i), zFunc); lines.forEach(line => { turtle.jump(line[0]); turtle.goto(line[1]); }); return i <= detail_z; } // Metaball Contour Lines. Created by Reinder Nijhoff 2020 - @reindernijhoff // The MIT License // https://turtletoy.net/turtle/104c4775c5 function ContourLines(z, step, zFunc) { const intersectSegmentZ = (z, v1, v2) => { if (v1[2] === v2[2]) return false; const t = (z - v1[2]) / (v2[2] - v1[2]); if (t <= 0 || t > 1) return false; return [v1[0]+(v2[0]-v1[0])*t, v1[1]+(v2[1]-v1[1])*t]; } const intersectTriangleZ = (z, p1, p2, p3) => { const p = []; const v1 = intersectSegmentZ(z, p1, p2); const v2 = intersectSegmentZ(z, p2, p3); const v3 = intersectSegmentZ(z, p3, p1); if (v1 && v2) p.push([v1, v2]); if (v1 && v3) p.push([v1, v3]); if (v2 && v3) p.push([v2, v3]); return p; } const result = []; for (let x = -100; x <= 100; x += step) { for (let y = -100; y <= 100; y += step) { const corners = [[x, y], [x+step, y], [x+step, y+step], [x, y+step]]; corners.forEach( c => c[2] = zFunc(c) ); const c3 = [x+step/2, y+step/2, zFunc([x+step/2, y+step/2])]; for (let i=0; i<4; i++) { result.push(...intersectTriangleZ(z, corners[i], corners[(i+1) & 3], c3)); } } } return result; }