Triskelion 🌀

A triskelion or triskeles is an ancient motif consisting of a triple spiral exhibiting rotational symmetry. The spiral design can be based on interlocking Archimedean spirals, or represent three bent human legs.

Triskelion 🌀 (variation)

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const rIncPerRev = 13; //min=2 max=50 step=1
const rMin = 30; //min=5 max=50 step=1
const correctCenter = 1; //min=0 max=1 step=1 (No, Yes)
const outline = 1; //min=0 max=1 step=1 (No, Yes)
const hatching = 1; //min=0 max=2 step=.1

// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);

// Global code will be evaluated once.
const turtle = new Turtle();
const polygons = new Polygons();

const add2 = (a, b) => [a[0]+b[0],a[1]+b[1]];
const lenSq2 = (a) => a[0]**2+a[1]**2;
const len2 = (a) => lenSq2(a)**.5;
const rot2 = (a) => [Math.cos(a), -Math.sin(a), Math.sin(a), Math.cos(a)];
const trans2 = (m, a) => [m[0]*a[0]+m[2]*a[1], m[1]*a[0]+m[3]*a[1]];

const spiralPts = spiral(rIncPerRev, rMin, Math.PI, Math.PI/3);
const startR = spiralPts[0][0];
const endR = len2(spiralPts[spiralPts.length - 1]);
const width  = startR + endR;
const height = (width**2 - (width/2)**2)**.5;

const pts = Array.from({length: 3}).flatMap((v, t) => spiralPts.map(p => trans2(rot2(t*4*Math.PI/3), p)).map(p => add2(trans2(rot2(t*4*Math.PI/3), [-width/2, height/3]), p)))
const centerOffset = correctCenter? pts.reduce((p, c) => [[Math.min(p[0][0], c[0]), Math.max(p[0][1], c[0])], [Math.min(p[1][0], c[1]), Math.max(p[1][1], c[1])]], [[0,0],[0,0]]).map(i => (-i[0]-i[1])/2): [0, 0];
const polygonize = () => {
    const p = polygons.create();
    p.addPoints(...pts.map(pt => add2(centerOffset, pt)));
    p.addHatching(1, hatching);
    polygons.draw(turtle, p);
}
if(hatching > 0) polygonize();

const walk = (i) => outline === 0? false: turtle[i==0?'jump':'goto'](add2(centerOffset, pts.shift())) || pts.length > 0;

function spiral(rIncreasePerRev, rMin, angleOne, angleTwo) {
    const result = [];
    const res = 100; //resolution
    
    const phaseOneMax = 2 * Math.PI * Math.ceil(rMin / rIncreasePerRev) + angleOne;
    const phaseTwoMax = 2 * Math.PI * Math.ceil(rMin / rIncreasePerRev) + angleTwo;
    let phase = 0;
    let i = 0;
    while(phase < phaseOneMax || phase < phaseTwoMax) {
        phase = 2 * Math.PI * i / res;
        const r = rIncreasePerRev * i / res;
        if(phase < phaseOneMax) result.unshift([r * -Math.cos(phase), r * Math.sin(phase)]);
        if(phase < phaseTwoMax) result.push([r * Math.cos(phase), r * -Math.sin(phase)]);
        i++;
    }
    result.unshift([(phaseOneMax / (2*Math.PI)) * rIncreasePerRev * -Math.cos(phaseOneMax), (phaseOneMax / (2*Math.PI)) * rIncreasePerRev * Math.sin(phaseOneMax)]);
    result.push([(phaseTwoMax / (2*Math.PI)) * rIncreasePerRev * Math.cos(phaseTwoMax), (phaseTwoMax / (2*Math.PI)) * rIncreasePerRev * -Math.sin(phaseTwoMax)]);
    return result;
}

////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// (Polygon binning by Lionel Lemarie 2021)
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////
function Polygons(){const t=[],s=25,e=Array.from({length:s**2},t=>[]),n=class{constructor(){this.cp=[],this.dp=[],this.aabb=[]}addPoints(...t){let s=1e5,e=-1e5,n=1e5,h=-1e5;(this.cp=[...this.cp,...t]).forEach(t=>{s=Math.min(s,t[0]),e=Math.max(e,t[0]),n=Math.min(n,t[1]),h=Math.max(h,t[1])}),this.aabb=[s,n,e,h]}addSegments(...t){t.forEach(t=>this.dp.push(t))}addOutline(){for(let t=0,s=this.cp.length;t<s;t++)this.dp.push(this.cp[t],this.cp[(t+1)%s])}draw(t){for(let s=0,e=this.dp.length;s<e;s+=2)t.jump(this.dp[s]),t.goto(this.dp[s+1])}addHatching(t,s){const e=new n;e.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);const h=Math.sin(t)*s,o=Math.cos(t)*s,a=200*Math.sin(t),i=200*Math.cos(t);for(let t=.5;t<150/s;t++)e.dp.push([h*t+i,o*t-a],[h*t-i,o*t+a]),e.dp.push([-h*t+i,-o*t-a],[-h*t-i,-o*t+a]);e.boolean(this,!1),this.dp=[...this.dp,...e.dp]}inside(t){let s=0;for(let e=0,n=this.cp.length;e<n;e++)this.segment_intersect(t,[.1,-1e3],this.cp[e],this.cp[(e+1)%n])&&s++;return 1&s}boolean(t,s=!0){const e=[];for(let n=0,h=this.dp.length;n<h;n+=2){const h=this.dp[n],o=this.dp[n+1],a=[];for(let s=0,e=t.cp.length;s<e;s++){const n=this.segment_intersect(h,o,t.cp[s],t.cp[(s+1)%e]);!1!==n&&a.push(n)}if(0===a.length)s===!t.inside(h)&&e.push(h,o);else{a.push(h,o);const n=o[0]-h[0],i=o[1]-h[1];a.sort((t,s)=>(t[0]-h[0])*n+(t[1]-h[1])*i-(s[0]-h[0])*n-(s[1]-h[1])*i);for(let n=0;n<a.length-1;n++)(a[n][0]-a[n+1][0])**2+(a[n][1]-a[n+1][1])**2>=.001&&s===!t.inside([(a[n][0]+a[n+1][0])/2,(a[n][1]+a[n+1][1])/2])&&e.push(a[n],a[n+1])}}return(this.dp=e).length>0}segment_intersect(t,s,e,n){const h=(n[1]-e[1])*(s[0]-t[0])-(n[0]-e[0])*(s[1]-t[1]);if(0===h)return!1;const o=((n[0]-e[0])*(t[1]-e[1])-(n[1]-e[1])*(t[0]-e[0]))/h,a=((s[0]-t[0])*(t[1]-e[1])-(s[1]-t[1])*(t[0]-e[0]))/h;return o>=0&&o<=1&&a>=0&&a<=1&&[t[0]+o*(s[0]-t[0]),t[1]+o*(s[1]-t[1])]}};return{list:()=>t,create:()=>new n,draw:(n,h,o=!0)=>{reducedPolygonList=function(n){const h={},o=200/s;for(var a=0;a<s;a++){const c=a*o-100,r=[0,c,200,c+o];if(!(n[3]<r[1]||n[1]>r[3]))for(var i=0;i<s;i++){const c=i*o-100;r[0]=c,r[2]=c+o,n[0]>r[2]||n[2]<r[0]||e[i+a*s].forEach(s=>{const e=t[s];n[3]<e.aabb[1]||n[1]>e.aabb[3]||n[0]>e.aabb[2]||n[2]<e.aabb[0]||(h[s]=1)})}}return Array.from(Object.keys(h),s=>t[s])}(h.aabb);for(let t=0;t<reducedPolygonList.length&&h.boolean(reducedPolygonList[t]);t++);h.draw(n),o&&function(n){t.push(n);const h=t.length-1,o=200/s;e.forEach((t,e)=>{const a=e%s*o-100,i=(e/s|0)*o-100,c=[a,i,a+o,i+o];c[3]<n.aabb[1]||c[1]>n.aabb[3]||c[0]>n.aabb[2]||c[2]<n.aabb[0]||t.push(h)})}(h)}}}