const size = 50; //min=2 max=50 step=1
const output = 0; //min=0 max=1 step=1 (Screen, Plotter)
const colors = output == 0? size: 1;
// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(output == 1? 1: 1/colors);

const distance = 2.5; //min=0 max=10 step=.5
const stack = 0; //min=0 max=1 step=1 (Plates, Planes)

// Global code will be evaluated once.
const polygons = new Polygons();
const polygonsOL = new Polygons();
const bales = Bales(colors, colors == 1? false: true);

const n = size;
const shapes = 4; //min=2 max=8 step=1 (Circle, Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon)
//const steps = 4; //min=3 max=10 step=1
const r = 50;

const shape = shapes == 1? ((Math.random() * 7) | 0) + 1: shapes;
const steps = shape == 2? Math.ceil(2 * Math.PI * r): shape;

// The walk function will be called until it returns false.
function walk(i) {
    const pts = circlePoints(r, 2 * Math.PI, i * 2 * Math.PI / (steps * n), steps).map(pt => 
        add2(
            [0, -(distance * n/2) + distance * i],
            mul2(pt, [1, .4])
        )
    );
    const mostLeft = pts.reduce((p, c) => c[0] < p[0]? c: p, [0,0]);
    const mostRight = pts.reduce((p, c) => c[0] < p[0]? p: c, [0,0]);
    
    const sidePts = pts.filter(pt => (pt[1] >= mostLeft[1] && pt[0] <= 0) || (pt[1] >= mostRight[1] && pt[0] >= 0));
    const sidePolygons = stack == 1? []: sidePts.map((pt, i, a) => [
        pt, a[(i+1)%a.length],
        add2(a[(i+1)%a.length], [0, distance]), add2(pt, [0, distance])
    ]);
    
    [pts, ...sidePolygons].forEach((pts, ii) => {
        if(colors > 1) {
            const p = polygons.create();
            p.addPoints(...pts);
            p.addHatching(1, .15);
            polygons.draw(bales[size - 1 - ((size*i/n) | 0)], p);
        }
    
        const ol = polygonsOL.create();
        ol.addPoints(...pts);
        ol.addOutline();
        if(colors == 1) ol.addHatching(2*i/n + ii, .15 + (3-(3*i/n)));
        polygonsOL.draw(bales[0], ol);
    });
    
    return i < n - 1;
}


function approx1(a,b,delta=0.0001) { return -delta < a-b && a-b < delta }

////////////////////////////////////////////////////////////////
// 2D Vector Math utility code - Created by several Turtletoy users
////////////////////////////////////////////////////////////////
function norm2(a) { return scale2(a, 1/len2(a)); }
function add2(a, b) { return [a[0]+b[0], a[1]+b[1]]; }
function sub2(a, b) { return [a[0]-b[0], a[1]-b[1]]; }
function mul2(a, b) { return [a[0]*b[0], a[1]*b[1]]; }
function scale2(a, s) { return [a[0]*s,a[1]*s]; }
function lerp2(a,b,t) { return [a[0]*(1-t) + b[0]*t, a[1]*(1-t) + b[1]*t]; }
function lenSq2(a) { return a[0]**2+a[1]**2; }
function len2(a) { return Math.sqrt(lenSq2(a)); }
function rot2(a) { return [Math.cos(a), -Math.sin(a), Math.sin(a), Math.cos(a)]; }
function trans2(m, a) { return [m[0]*a[0]+m[2]*a[1], m[1]*a[0]+m[3]*a[1]]; } //Matrix(2x1) x Matrix(2x2)
function dist2(a,b) { return Math.hypot(...sub2(a,b)); }
function dot2(a,b) { return a[0]*b[0]+a[1]*b[1]; }
function cross2(a,b) { return a[0]*b[1] - a[1]*b[0]; }
function multiply2(a2x2, a) { return [(a[0]*a2x2[0])+(a[1]*a2x2[1]),(a[0]*a2x2[2])+(a[1]*a2x2[3])]; } //Matrix(2x2) x Matrix(1x2)
function intersect_info2(as, ad, bs, bd) {
    const d = [bs[0] - as[0], bs[1] - as[1]];
    const det = bd[0] * ad[1] - bd[1] * ad[0];
    if(det === 0) return false;
    const res = [(d[1] * bd[0] - d[0] * bd[1]) / det, (d[1] * ad[0] - d[0] * ad[1]) / det];
    return [...res, add2(as, scale2(ad, res[0]))];
}
function intersect_ray2(a, b, c, d) {
    const i = intersect_info2(a, b, c, d);
    return i === false? i: i[2];
}
function segment_intersect2(a,b,c,d, inclusive = true) {
    const i = intersect_info2(a, sub2(b, a), c, sub2(d, c));
    if(i === false) return false;
    const t = inclusive? 0<=i[0]&&i[0]<=1&&0<=i[1]&&i[1]<=1: 0<i[0]&&i[0]<1&&0<i[1]&&i[1]<1;
    return t?i[2]:false;
}
function approx2(a,b,delta=0.0001) { return len2(sub2(a,b)) < delta }
function eq2(a,b) { return a[0]==b[0]&&a[1]==b[1]; }
function clamp2(a, tl, br) { return [Math.max(Math.min(br[0], a[0]), tl[0]), Math.max(Math.min(br[1], a[1]), tl[1])]; }
function nearSq2(test, near, delta = .0001) {
    return near[0] - delta < test[0] && test[0] < near[0] + delta &&
           near[1] - delta < test[1] && test[1] < near[1] + delta;
}
function intersectCircles2(p1, r1, p2, r2) {
    let d = ((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)**.5;
    if (!(Math.abs(r1 - r2) <= d && d <= r1 + r2)) {
        return []; // no intersection, to far apart or total overlap
    }
    
    const calc = (left, right) => [[(left[0] + right[0]) / 2 + (r1**2 - r2**2) * (right[0] - left[0]) / (2 * d**2), (2 * (r1**2 + r2**2) / d**2 - ((r1**2 - r2**2)**2) / d**4 - 1)**.5 * (right[1] - left[1]) / 2]].map(t => [t[0] + t[1], t[0] - t[1]]).pop();
    
    let xs = calc(p1, p2);
    let ys = calc([...p1].reverse(), [...p2].reverse()).reverse();
    
    return [[xs[0], ys[0]], [xs[1], ys[1]]];
}
function circlePointAtDirection2(circle_center, radius, direction) { return add2(circle_center, scale2(direction, radius/len2(direction))); }

////////////////////////////////////////////////////////////////
// Start of some path utility code - Created by Jurgen Westerhof 2023
////////////////////////////////////////////////////////////////
function circlePoints(radius, extend = 2 * Math.PI, clockWiseStart = 0, steps = null, includeLast = false) { return [steps == null? (radius*extend+1)|0: steps].map(steps => Array.from({length: steps}).map((v, i, a) => [radius * Math.cos(clockWiseStart + extend*i/(a.length-(includeLast?1:0))), radius * Math.sin(clockWiseStart + extend*i/(a.length-(includeLast?1:0)))])).pop(); }
function pts2Edges(pts) { return pts.map((v, i, a) => [v, a[(i+1)%a.length]]); }
function drawPath(turtle, pts) { return pts.forEach((pt, i) => turtle[i == 0? 'jump':'goto'](pt)); }
function drawTour(turtle, pts) { return drawPath(turtle, pts.concat([pts[0]])); }
function drawPoint(turtle, pt) { return drawTour(turtle, circlePoints(.5).map(p => add2(p, pt))); }
function isInPolygon(edges, pt) { return edges.map(edge => intersect_info2(edge[0], sub2(edge[1], edge[0]), pt, [0, 300])).filter(ii => ii !== false && 0 <= ii[0] && ii[0] <= 1 && 0 < ii[1]).length % 2 == 1; }
function isInVectorTour(vectors, pt) { return vectors.map(v => intersect_info2(...v, pt[0], pt[1])).filter(ii => ii !== false && 0 <= ii[0] && ii[0] < 1 && 0 <= ii[1]).length % 2 == 1; }
function tourToVectors(path) { return path.map((v, i, a) => [v, sub2(a[(i+1)%a.length], v)]); }
function thickLinePaths(from, to, thickness) { return [trans2(rot2(Math.atan2(...sub2(to, from))), [thickness/2, 0])].map(v => [[add2(from, v), add2(to, v)], [sub2(from, v), sub2(to, v)]]).pop();}

// Fisher-Yates (aka Knuth) Shuffle
// https://stackoverflow.com/questions/2450954/how-to-randomize-shuffle-a-javascript-array#2450976
function shuffle(array) {
  let currentIndex = array.length,  randomIndex;

  // While there remain elements to shuffle.
  while (currentIndex > 0) {

    // Pick a remaining element.
    randomIndex = Math.floor(Math.random() * currentIndex);
    currentIndex--;

    // And swap it with the current element.
    [array[currentIndex], array[randomIndex]] = [
      array[randomIndex], array[currentIndex]];
  }

  return array;
}

////////////////////////////////////////////////////////////////
// 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)}}}

////////////////////////////////////////////////////////////////
// Bale utility code - Created by Jurgen Westerhof 2022
// https://turtletoy.net/turtle/7269af8a23
// Abusing the opacity, usage:
//      Canvas.setpenopacity(1/baleSize);
//      const bales = Array.apply(null,{length: baleSize}).map(b => new Bale(baleSize--);
// Then use bales[x] wherever you would use a turtle object to 'draw'
// in 'color' x (i.e Polygon hatching with a bale object and .15 interspacing)
////////////////////////////////////////////////////////////////
function Bale(n) {
    class Bale {
        constructor(n) { this.turtles = Array.apply(null,{length: n}).map(i => new Turtle()); }
        
        back(e)         { this.turtles.map(t => t.back(e)); return this; }
        backward(e)     { this.turtles.map(t => t.backward(e)); return this; }
        bk(e)           { this.turtles.map(t => t.bk(e)); return this; }
        fd(e)           { this.turtles.map(t => t.fd(e)); return this; }
        forward(e)      { this.turtles.map(t => t.forward(e)); return this; }

        left(e)         { this.turtles.map(t => t.left(e)); return this; }
        lt(e)           { this.turtles.map(t => t.lt(e)); return this; }
        right(e)        { this.turtles.map(t => t.right(e)); return this; }
        rt(e)           { this.turtles.map(t => t.rt(e)); return this; }

        seth(e)         { this.turtles.map(t => t.seth(e)); return this; }
        setheading(e)   { this.turtles.map(t => t.setheading(e)); return this; }

        setx(e)         { this.turtles.map(t => t.setx(e)); return this; }
        sety(e)         { this.turtles.map(t => t.sety(e)); return this; }

        setpos(x, y)        { this.turtles.map(t => t.setpos(x, y)); return this; }
        setposition(x, y)   { this.turtles.map(t => t.setposition(x, y)); return this; }

        toradians(e)    { this.turtles.map(t => t.toradians(e)); return this; }
        degrees(e)      { this.turtles.map(t => t.degrees(e)); return this; }

        goto(x, y)      { this.turtles.map(t => t.goto(x, y)); return this; }
        jmp(x, y)       { this.turtles.map(t => t.jmp(x, y)); return this; }
        jump(x, y)      { this.turtles.map(t => t.jump(x, y)); return this; }

        circle(radius, extent, steps) { this.turtles.map(t => t.circle(radius, extent, steps)); return this; }

        clone()         { let b = new Bale(this.turtle.length); this.turtles.map((t, k) => b.turtles[k] = t.clone()); return b; }

        h()             { return this.turtles[0].h(); }
        heading()       { return this.turtles[0].heading(); }
        
        home()          { this.turtles.map(t => t.home()); return this; }
        
        isdown()        { return this.turtles[0].isdown(); }

        pos()           { return this.turtles[0].pos(); }
        position()      { return this.turtles[0].position(); }

        pd()            { this.turtles.map(t => t.pd()); return this; }
        pendown()       { this.turtles.map(t => t.pendown()); return this; }
        penup()         { this.turtles.map(t => t.penup()); return this; }
        pu()            { this.turtles.map(t => t.pu()); return this; }
        down()          { this.turtles.map(t => t.down()); return this; }
        up()            { this.turtles.map(t => t.up()); return this; }

        radians()       { this.turtles.map(t => t.radians()); return this; }

        x()             { return this.turtles[0].x(); }
        xcor()          { return this.turtles[0].xcor(); }
        y()             { return this.turtles[0].y(); }
        ycor()          { return this.turtles[0].ycor(); }
    }
    return new Bale(n);
}
function Bales(count, includeWhite = false) {
    if(count == 1) return [new Bale(1)];
    const getExponent = (base, target) => Math.log(target) / Math.log(base);
    const baleSize = count - (includeWhite?1:0);
    const n = Array.apply(null,{length: baleSize}).map((v,k) => Math.round(getExponent(1 - 1/count, 1 - (count - k == count?.99:(baleSize - k)/baleSize))));
    if(includeWhite) n.push(0);
    return n.map(i => new Bale(i));
}