const shadesOfGrey = 6; //min=2 max=16 step=2 Fewer shades equals faster drawing
const display = 4; //min=0 max=4 step=1 (Single error-diffusion dithering, Single ordered dithering; using Bayer matrix, Showcase first 4 error-diffusion dithering, Showcase first 4; using Bayer matrix, Showcase threshold; Floyd-Steinberg; 1st and 3rd order bayer ordered Dithering )
const ed_dither = 2; //min=0 max=10 step=1 (None; threshold, Simple, Floyd-Steinberg, Atkinson, Jarvis Judice and Ninke, Stucki, Sierra, Burkes, False Floyd-Steinberg, Two-row Sierra, Sierra Lite)
const o_dither_order = 3; //min=0 max=4 step=1 (None; threshold, 1, 2, 3, 4)

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

// Global code will be evaluated once.
init();
const bales = Bales(shadesOfGrey);

const decompressedImage = Array.from(StringToUint8(getImageData()));

const errorDiffusionDithers = [
    //none
    [],
    //simple
    [[[1,0],.5],[[0,1],.5]],
    //Floyd-Steinberg
    [
        [[ 1, 0], 7/16],
        [[-1, 1], 3/16],
        [[ 0, 1], 5/16],
        [[ 1, 1], 1/16]
    ],
    //Atkinson
    [
        [[ 1, 0], 1/8],
        [[ 2, 0], 1/8],
        [[-1, 1], 1/8],
        [[ 0, 1], 1/8],
        [[ 1, 1], 1/8],
        [[ 0, 2], 1/8],
    ],
    //Jarvis, Judice and Ninke
    [
        [[ 1, 0],  7/48],
        [[ 2, 0],  5/48],
        [[-2, 1],  3/48],
        [[-1, 1],  5/48],
        [[ 0, 1],  7/48],
        [[ 1, 1],  5/48],
        [[ 2, 1],  3/48],
        [[-2, 2],  1/48],
        [[-1, 2],  3/48],
        [[ 0, 2],  5/48],
        [[ 1, 2],  3/48],
        [[ 2, 2],  1/48],
    ],
    //Stucki
    [
        [[ 1, 0],  8/42],
        [[ 2, 0],  4/42],
        [[-2, 1],  2/42],
        [[-1, 1],  4/42],
        [[ 0, 1],  8/42],
        [[ 1, 1],  4/42],
        [[ 2, 1],  2/42],
        [[-2, 2],  1/42],
        [[-1, 2],  2/42],
        [[ 0, 2],  4/42],
        [[ 1, 2],  2/42],
        [[ 2, 2],  1/42],
    ],
    //Sierra
    [
        [[ 1, 0],  5/32],
        [[ 2, 0],  3/32],
        [[-2, 1],  2/32],
        [[-1, 1],  4/32],
        [[ 0, 1],  5/32],
        [[ 1, 1],  4/32],
        [[ 2, 1],  2/32],
        [[-1, 2],  2/32],
        [[ 0, 2],  3/32],
        [[ 1, 2],  2/32],
    ],
    //Burkes
    [
        [[ 1, 0], 8/32],
        [[ 2, 0], 4/32],
        [[-2, 1], 2/32],
        [[-1, 1], 4/32],
        [[ 0, 1], 8/32],
        [[ 1, 1], 4/32],
        [[ 2, 1], 2/32],
    ],
    //False Floyd-Steinberg
    [
        [[ 1, 0], 3/8],
        [[ 0, 1], 3/8],
        [[ 1, 1], 2/8],
    ],
    //Two-row Sierra
    [
        [[ 1, 0], 4/16],
        [[ 2, 0], 3/16],
        [[-2, 1], 1/16],
        [[-1, 1], 2/16],
        [[ 0, 1], 3/16],
        [[ 1, 1], 2/16],
        [[ 2, 1], 1/16],
    ],
    //Sierra Lite
    [
        [[ 1, 0], 2/4],
        [[-1, 1], 1/4],
        [[ 0, 1], 1/4],
    ],
];

function applyDither(decompressedImage, dither) {
    const idx = (x,y) => x + y * 200;
    const factor = shadesOfGrey - 1;
    for(let y = 0; y < 200; y++) {
        for(let x = 0; x < 200; x++) {
            const curVal = decompressedImage[idx(x, y)];
            const newVal = Math.min(255, Math.round(factor * curVal / 255) * (255 / factor));
            decompressedImage[idx(x, y)] = newVal;
            const quantError = curVal - newVal;
            dither.forEach(e => {
                const px = [x + e[0][0], y + e[0][1]];
                if(px[0] < 0 || 200 <= px[0] || px[1] < 0 || 200 <= px[1]) return;
                decompressedImage[idx(...px)] += quantError * e[1];
            });
        }
    }
    
    return decompressedImage;
}

function drawPixel(turtle, location, hatchDirection=0, hatchDistance=1, size=10) {
    const vertices = [[-.5,-.5],[.5,-.5],[.5,.5],[-.5,.5]].map(pt => V.add(location, V.scale(pt, size)));

    const rot = V.rot2d(hatchDirection);
    const invRot = V.rot2d(-hatchDirection);
    
    const [from, to] = [
        vertices.map(pt => V.trans(invRot, pt))
                .reduce((a, c) => [Math.min(a[0], c[1]), Math.max(a[1], c[1])], [Number.MAX_SAFE_INTEGER, Number.MIN_SAFE_INTEGER])
    ].map(yMinMax => [Math.floor(yMinMax[0]/hatchDistance), Math.ceil(yMinMax[1]/hatchDistance)]).pop().map(v => v * hatchDistance);
    
    for(let y = from; y <= to; y += hatchDistance) {
        const line = [[-100*Math.SQRT2, y], [100*Math.SQRT2, y]].map(pt => V.trans(rot, pt));
        const is = vertices.map((e,i,a) => Intersection.segment(...line, e, a[(i+1)%a.length])).filter(v => v);
        if(is.length == 2) {
            PT.draw(turtle, is);
        }
    }
}

function displayPixel(x, y, scale, lumination) {
    const baleIdx = lumination*(shadesOfGrey-1) | 0;
    drawPixel(bales[baleIdx], V.scale([x - 99.5, y - 99.5], .5), 1, .17, scale);
}

const images = errorDiffusionDithers.map((e, i) => applyDither(decompressedImage.map(v => v), e));
const dithered_8bpps = [images[0].map(v => v)].concat([1, 2, 3, 4].map(e => ordered_dither(decompressedImage, e, getLut(shadesOfGrey))));


// The walk function will be called until it returns false.
function walk(i) {
    const x = i % 200;
    const y = i / 200 | 0;

    switch(display) {
        case 0: //single error-diffusion
            const lumination = images[ed_dither][i] / 255;
        
            displayPixel(x*2-99.5, y*2-99.5, 1, lumination);
            break;
        case 1: //ordered dithering
            const lumination2 = dithered_8bpps[o_dither_order][i] / 255;
        
            displayPixel(x*2-99.5, y*2-99.5, 1, lumination2);
            break;
        case 2: //showcase 4 error-diffusions
            [[-100, -100], [100, -100], [-100, 100], [100, 100]].forEach((pt, j) => {
                const lumination = images[j][i] / 255;
                
                displayPixel(x+pt[0], y+pt[1], .5, lumination);
            })
            break;
        case 3: //showcase 3 ordered dithering
            [[-100, -100], [100, -100], [-100, 100], [100, 100]].forEach((pt, j) => {
                const lumination = dithered_8bpps[j][i] / 255;
                
                displayPixel(x+pt[0], y+pt[1], .5, lumination);
            })
            break;
        case 4: //showcase none, fl-st, 1st bayer, 3rd bayer
            [[-100, -100], [100, -100], [-100, 100], [100, 100]].forEach((pt, j) => {
                const lumination = (j < 2? images[j][i]: dithered_8bpps[(j - 2) * 2 + 1][i]) / 255;
                
                displayPixel(x+pt[0], y+pt[1], .5, lumination);
            })
            break;
    }

    return i < 200**2-1;
}

//https://stackoverflow.com/questions/77525608/ordered-dithering-to-4-colors-with-javascript#77526060
function ordered_dither(image_array, order, lut)
{
    const matrix = M.bayer(order);
    const ai = image_array.map(v => v);
    const idx = (x,y) => x + y * 200;
    // image_array_2d is a 2d array of grayscale values from 0-255
    // matrix is a 2d array with values normalized to be between 0.0 and 1.0
    // LUT is an arry of 8-bit values, in this case [0, 85, 170, 255]
    const image_height = 200;
    const image_width  = 200;
    for (let y = 0; y < image_height; y++) {
        for (let x = 0; x < image_width; x++) {
            let pixel_value = ai[idx(x, y)];

            // find closest value to pixel in LUT
            let value_current = lut[lut.length - 1], value_prev = lut[lut.length - 2];
            for (let i = 1; i < lut.length; i++) {
                if (pixel_value < lut[i]) {
                    value_current = lut[i]
                    value_prev = lut[i - 1];
                    break;
                }
            }

            const threshold = value_prev + (value_current - value_prev) * matrix[y % matrix.length][x % matrix.length] / 2**(2*order);
            let new_value = 0
            new_value = pixel_value > threshold ? value_current : value_prev
            
            ai[idx(x, y)] = new_value
        }
    }

    return ai;
}

function getLut(number_of_colors, max = 255, min = 0) {
    if(number_of_colors == 1) return [((max+min)/2)|0];
    return [(max-min) / (number_of_colors - 1)].map(step => Array.from({length: number_of_colors}, (e,i) => (min + i * step) | 0)).pop();
}

function StringToUint8(str) {
  const u8a = new Uint8Array(str.length);
  for(let i = 0; i < str.length; i++) {
    u8a[i] = str.charCodeAt(i);
  }
  return u8a;
}

function init() {
    ///////////////////////////////////////////////////////
    // Vector functions - Created by Jurgen Westerhof 2024
    // https://turtletoy.net/turtle/d068ad6040
    ///////////////////////////////////////////////////////
    class Vector {
        static add  (a,b) { return a.map((v,i)=>v+b[i]); }
        static sub  (a,b) { return a.map((v,i)=>v-b[i]); }
        static mul  (a,b) { return a.map((v,i)=>v*b[i]); }
        static div  (a,b) { return a.map((v,i)=>v/b[i]); }
        static scale(a,s) { return a.map(v=>v*s); }
    
        static det(m)                { return m.length == 1? m[0][0]: m.length == 2 ? m[0][0]*m[1][1]-m[0][1]*m[1][0]: m[0].reduce((r,e,i) => r+(-1)**(i+2)*e*this.det(m.slice(1).map(c => c.filter((_,j) => i != j))),0); }
        static angle(a)              { return Math.PI - Math.atan2(a[1], -a[0]); } //compatible with turtletoy heading
        static rot2d(angle)          { return [[Math.cos(angle), -Math.sin(angle)], [Math.sin(angle), Math.cos(angle)]]; }
        static rot3d(yaw,pitch,roll) { return [[Math.cos(yaw)*Math.cos(pitch), Math.cos(yaw)*Math.sin(pitch)*Math.sin(roll)-Math.sin(yaw)*Math.cos(roll), Math.cos(yaw)*Math.sin(pitch)*Math.cos(roll)+Math.sin(yaw)*Math.sin(roll)],[Math.sin(yaw)*Math.cos(pitch), Math.sin(yaw)*Math.sin(pitch)*Math.sin(roll)+Math.cos(yaw)*Math.cos(roll), Math.sin(yaw)*Math.sin(pitch)*Math.cos(roll)-Math.cos(yaw)*Math.sin(roll)],[-Math.sin(pitch), Math.cos(pitch)*Math.sin(roll), Math.cos(pitch)*Math.cos(roll)]]; }
        static trans(matrix,a)       { return a.map((v,i) => a.reduce((acc, cur, ci) => acc + cur * matrix[ci][i], 0)); }
        //Mirror vector a in a ray through [0,0] with direction mirror
        static mirror2d(a,mirror)    { return [Math.atan2(...mirror)].map(angle => this.trans(this.rot2d(angle), this.mul([-1,1], this.trans(this.rot2d(-angle), a)))).pop(); }

        static approx(a,b,p) { return this.len(this.sub(a,b)) < (p === undefined? .001: p); }
        static norm  (a)     { return this.scale(a,1/this.len(a)); }
        static len   (a)     { return Math.hypot(...a); }
        static lenSq (a)     { return a.reduce((a,c)=>a+c**2,0); }
        static lerp  (a,b,t) { return a.map((v, i) => v*(1-t) + b[i]*t); }
        static dist  (a,b)   { return Math.hypot(...this.sub(a,b)); }
        
        static dot  (a,b)   { return a.reduce((a,c,i) => a+c*b[i], 0); }
        static cross(...ab) { return ab[0].map((e, i) => ab.map(v => v.filter((ee, ii) => ii != i))).map((m,i) => (i%2==0?-1:1)*this.det(m)); }
    }
    this.V = Vector;
    
    class Intersection2D {
        //a-start, a-direction, b-start, b-direction
        //returns false on no intersection or [[intersection:x,y], scalar a-direction, scalar b-direction
        static info(as, ad, bs, bd) { const d = V.sub(bs, as), det = -V.det([bd, ad]); if(det === 0) return false; const res = [V.det([d, bd]) / det, V.det([d, ad]) / det]; return [V.add(as, V.scale(ad, res[0])), ...res]; }
        static ray(a, b, c, d) { return this.info(a, b, c, d); }
        static segment(a,b,c,d, inclusiveStart = true, inclusiveEnd = true) { const i = this.info(a, V.sub(b, a), c, V.sub(d, c)); return i === false? false: ( (inclusiveStart? 0<=i[1] && 0<=i[2]: 0<i[1] && 0<i[2]) && (inclusiveEnd?   i[1]<=1 && i[2]<=1: i[1]<1 && i[2]<1) )?i[0]:false;}
        static tour(tour, segmentStart, segmentDirection) { return tour.map((e, i, a) => [i, this.info(e, V.sub(a[(i+1)%a.length], e), segmentStart, segmentDirection)]).filter(e => e[1] !== false && 0 <= e[1][1] && e[1][1] <= 1).filter(e => 0 <= e[1][2]).map(e => ({position: e[1][0],tourIndex: e[0],tourSegmentPortion: e[1][1],segmentPortion: e[1][2],}));}
        static inside(tour, pt) { return tour.map((e,i,a) => this.segment(e, a[(i+1)%a.length], pt, [Number.MAX_SAFE_INTEGER, 0], true, false)).filter(e => e !== false).length % 2 == 1; }
        static circles(centerA, radiusA, centerB, radiusB) {const result = {intersect_count: 0,intersect_occurs: true,one_is_in_other: false,are_equal: false,point_1: [null, null],point_2: [null, null],};const dx = centerB[0] - centerA[0];const dy = centerB[1] - centerA[1];const dist = Math.hypot(dy, dx);if (dist > radiusA + radiusB) {result.intersect_occurs = false;}if (dist < Math.abs(radiusA - radiusB) && !N.approx(dist, Math.abs(radiusA - radiusB))) {result.intersect_occurs = false;result.one_is_in_other = true;}if (V.approx(centerA, centerB) && radiusA === radiusB) {result.are_equal = true;}if (result.intersect_occurs) {const centroid = (radiusA**2 - radiusB**2 + dist * dist) / (2.0 * dist);const x2 = centerA[0] + (dx * centroid) / dist;const y2 = centerA[1] + (dy * centroid) / dist;const prec = 10000;const h = (Math.round(radiusA**2 * prec)/prec - Math.round(centroid**2 * prec)/prec)**.5;const rx = -dy * (h / dist);const ry = dx * (h / dist);result.point_1 = [x2 + rx, y2 + ry];result.point_2 = [x2 - rx, y2 - ry];if (result.are_equal) {result.intersect_count = null;} else if (result.point_1.x === result.point_2.x && result.point_1.y === result.point_2.y) {result.intersect_count = 1;} else {result.intersect_count = 2;}}return result;}
    }
    this.Intersection = Intersection2D;
    
    class PathTools {
        static bezier(p1, cp1, cp2, p2, steps = null) {steps = (steps === null? (V.len(V.sub(cp1, p1)) + V.len(V.sub(cp2, cp1)) + V.len(V.sub(p2, cp2))) | 0: steps) - 1;return Array.from({length: steps + 1}).map((v, i, a, f = i/steps) => [[V.lerp(p1, cp1, f),V.lerp(cp1, cp2, f),V.lerp(cp2, p2, f)]].map(v => V.lerp(V.lerp(v[0], v[1], f), V.lerp(v[1], v[2], f), f))[0]);}
        // https://stackoverflow.com/questions/18655135/divide-bezier-curve-into-two-equal-halves#18681336
        static splitBezier(p1, cp1, cp2, p2, t=.5) {const e = V.lerp(p1, cp1, t);const f = V.lerp(cp1, cp2, t);const g = V.lerp(cp2, p2, t);const h = V.lerp(e, f, t);const j = V.lerp(f, g, t);const k = V.lerp(h, j, t);return [[p1, e, h, k], [k, j, g, p2]];}
        static circular(radius,verticeCount,rotation=0) {return Array.from({length: verticeCount}).map((e,i,a,f=i*2*Math.PI/verticeCount+rotation) => [radius*Math.cos(f),radius*Math.sin(f)])}
        static circle(r){return this.circular(r,Math.max(12, r*2*Math.PI|0));}
        static arc(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(); }
        static draw(turtle, path) {path.forEach((pt, i) => turtle[i==0?'jump':'goto'](pt));}
        static drawTour(turtle, path) {this.draw(turtle, path.concat([path[0]]));}
        static drawPoint(turtle, pt, r = .1) {this.drawTour(turtle, this.circle(r).map(e => V.add(e, pt)));}
        static drawArrow(turtle, s, d, width = 6, length = 3) {turtle.jump(s);const arrowHeadBase = V.add(s,d);turtle.goto(arrowHeadBase);turtle.goto(V.add(arrowHeadBase, V.trans(V.rot2d(-V.angle(d)), [-length, width/2])));turtle.jump(V.add(arrowHeadBase, V.trans(V.rot2d(-V.angle(d)), [-length, -width/2])));turtle.goto(arrowHeadBase);}
        static circlesTangents(c1_center, c1_radius, c2_center, c2_radius, internal = false) {let middle_circle = [V.scale(V.sub(c1_center, c2_center), .5)].map(hwp => [V.add(c2_center, hwp), V.len(hwp)]).pop();if(!internal && c1_radius == c2_radius) {let target = V.sub(c2_center, c1_center);let scaledTarget = V.scale(target, c1_radius/V.len(target));let partResult = [V.add(c1_center, V.trans(V.rot2d(Math.PI/2), scaledTarget)),V.add(c1_center, V.trans(V.rot2d(Math.PI/-2), scaledTarget))];return [partResult,partResult.map(pt => V.add(pt, target))]}let swap = !internal && c2_radius > c1_radius;if(swap) {let t = [[...c1_center], c1_radius];c1_center = c2_center;c1_radius = c2_radius;c2_center = t[0];c2_radius = t[1];}let internal_waypoints = intersectCircles2(c1_center, c1_radius + (internal?c2_radius:-c2_radius), ...middle_circle);if(internal_waypoints.length == 0) return [];const circlePointAtDirection2 = (circle_center, radius, direction) => V.add(circle_center, V.scale(direction, radius/V.len(direction)));const result = [[circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints[0], c1_center)),circlePointAtDirection2(c1_center, c1_radius, V.sub(internal_waypoints[1], c1_center))],[circlePointAtDirection2(c2_center, c2_radius, internal? V.sub(c1_center, internal_waypoints[0]): V.sub(internal_waypoints[0], c1_center)),circlePointAtDirection2(c2_center, c2_radius, internal? V.sub(c1_center, internal_waypoints[1]): V.sub(internal_waypoints[1], c1_center))]];return swap? [[result[1][1],result[1][0]],[result[0][1],result[0][0]]]: result;}
    }

    this.PT = PathTools;
    
    class Complex {
        static add(a,b)     { return V.add(a,b); }
        static sub(a,b)     { return V.sub(a,b); }
        static scale(a,s)   { return V.scale(a,s); }
        static mult(a,b)    { return [a[0]*b[0]-a[1]*b[1],a[0]*b[1]+a[1]*b[0]]; }
        static sqrt(a)      { return [[Math.hypot(...a)**.5, Math.atan2(...a.reverse()) / 2]].map(ra => [ra[0]*Math.cos(ra[1]), ra[0]*Math.sin(ra[1])]).pop(); }
    }
    this.C = Complex;
    
    class Numbers {
        static approx(a,b,p)        { return Math.abs(a-b) < (p === undefined? .001: p); }
        static clamp(a, min, max)   { return Math.min(Math.max(a, min), max); }
    }
    this.N = Numbers;
    
    class Matrix {
        static bayer(order) { return [...Array(1<<order)].map((_,y,a) => { const g = (k=order,x)=>k--&&4*g(k,x)|2*(x>>k)+3*(y>>k&1)&3; return a.map(g); }); }
        static rotate(m) { return m[0].map((e, i) => m.map(r => r[i]).reverse()); }
        static rotateCCW(m) { return m[0].map((e, i) => m.map(r => r[r.length-1-i])); }
        static add(a,b) { return a.map((e, c) => e.map((e, r) => a[c][r] + b[c][r])); }
        static sub(a,b) { return a.map((e, c) => e.map((e, r) => a[c][r] - b[c][r])); }
        static multiply(a,b) { return Array.from({length: b.length}, (e,resCol) => Array.from({length: a[0].length}, (e,resRow) => b[resCol].reduce((acc, c, bRow) => acc + a[bRow][resRow] * b[resCol][bRow], 0)));}
        static scale(a,s) { return a.map((e, c) => e.map((e, r) => a[c][r] * s)); }
        static random(c,r,fillFn = Math.random) { return Array.from({length: c}, (e,i) => Array.from({length: r}, e => fillFn(c, r))); }
        static identity(d) { return Array.from({length: d}, (e,c) => Array.from({length: d}, (e, r) => c==r?1:0 )); }
        static log(m, name, logFn = console.log) { if(name != undefined) logFn(name); if(m === undefined || (typeof m == 'object' && (m[0] === undefined || m[0][0] === undefined))) { return logFn(`Failed to log matrix:`, m); } logFn(m[0].map((e,r) => m.map((e,c) => m[c][r]).join(', ')).join('\n')); }
        static invert(m) { let _A = m.map(col => col.map(cell => cell));/*clone matrix*/let temp;const N = _A.length;const E = Array.from({length: N}, (e,i) => Array.from({length: _A[0].length}, (e,j) => i==j?1:0));for (let k = 0; k < N; k++) {temp = _A[k][k];for (let j = 0; j < N; j++) {_A[k][j] /= temp;E[k][j] /= temp;}for (let i = k + 1; i < N; i++) {temp = _A[i][k];for (let j = 0; j < N; j++) {_A[i][j] -= _A[k][j] * temp;E[i][j] -= E[k][j] * temp;}}}for (let k = N - 1; k > 0; k--) {for (let i = k - 1; i >= 0; i--) {temp = _A[i][k];for (let j = 0; j < N; j++) {_A[i][j] -= _A[k][j] * temp;E[i][j] -= E[k][j] * temp;}}}return E; }
        static determinant(m) { return m.length == 1 ?m[0][0] :m.length == 2 ? m[0][0]*m[1][1]-m[0][1]*m[1][0] :m[0].reduce((r,e,i) => r+(-1)**(i+2)*e*this.determinant(m.slice(1).map(c => c.filter((_,j) => i != j))), 0)}
        static flip(m) { return Array.from({length: m[0].length}, (_, r) => Array.from({length: m.length}, (e, c) => m[c][r])); }
        static sum(m) { return m.reduce((a, c) => a + c.reduce((aa, cc) => aa + cc, 0), 0); }
    }
    this.M = Matrix;
}

////////////////////////////////////////////////////////////////
// Bale utility code - Created by Jurgen Westerhof 2022
// https://turtletoy.net/turtle/beb59d67ae
// Abusing the opacity, usage:
//      Canvas.setpenopacity(1/paletteSize);
//      const bales = Bales(paletteSize); // Bales(count, includeFullTransparent = true, turtleClass = null)
// 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)
//      bales[x].jump(0,0);
//      bales[x].goto(40,0);
////////////////////////////////////////////////////////////////
function Bale(n, turtleClass = null) {class Bale {constructor(n, turtleClass = null) { this.turtles = Array.apply(null,{length: n}).map(i => turtleClass == null? new Turtle(): new turtleClass()); }back(e)         { this.turtles.forEach(t => t.back(e)); return this; }backward(e)     { this.turtles.forEach(t => t.backward(e)); return this; }bk(e)           { this.turtles.forEach(t => t.bk(e)); return this; }fd(e)           { this.turtles.forEach(t => t.fd(e)); return this; }forward(e)      { this.turtles.forEach(t => t.forward(e)); return this; }left(e)         { this.turtles.forEach(t => t.left(e)); return this; }lt(e)           { this.turtles.forEach(t => t.lt(e)); return this; }right(e)        { this.turtles.forEach(t => t.right(e)); return this; }rt(e)           { this.turtles.forEach(t => t.rt(e)); return this; }seth(e)         { this.turtles.forEach(t => t.seth(e)); return this; }setheading(e)   { this.turtles.forEach(t => t.setheading(e)); return this; }setx(e)         { this.turtles.forEach(t => t.setx(e)); return this; }sety(e)         { this.turtles.forEach(t => t.sety(e)); return this; }setpos(x, y)        { this.turtles.forEach(t => t.setpos(x, y)); return this; }setposition(x, y)   { this.turtles.forEach(t => t.setposition(x, y)); return this; }toradians(e)    { this.turtles.forEach(t => t.toradians(e)); return this; }degrees(e)      { this.turtles.forEach(t => t.degrees(e)); return this; }goto(x, y)      { this.turtles.forEach(t => t.goto(x, y)); return this; }jmp(x, y)       { this.turtles.forEach(t => t.jmp(x, y)); return this; }jump(x, y)      { this.turtles.forEach(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.turtles.length); this.turtles.forEach((t, k) => b.turtles[k] = t.clone()); return b; }h()             { return this.turtles.length == 0? null: this.turtles[0].h(); }heading()       { return this.turtles.length == 0? null: this.turtles[0].heading(); }home()          { this.turtles.forEach(t => t.home()); return this; }isdown()        { return this.turtles.length == 0? null: this.turtles[0].isdown(); }pos()           { return this.turtles.length == 0? null: this.turtles[0].pos(); }position()      { return this.turtles.length == 0? null: this.turtles[0].position(); }pd()            { this.turtles.forEach(t => t.pd()); return this; }pendown()       { this.turtles.forEach(t => t.pendown()); return this; }penup()         { this.turtles.forEach(t => t.penup()); return this; }pu()            { this.turtles.forEach(t => t.pu()); return this; }down()          { this.turtles.forEach(t => t.down()); return this; }up()            { this.turtles.forEach(t => t.up()); return this; }radians()       { this.turtles.forEach(t => t.radians()); return this; }x()             { return this.turtles.length == 0? null: this.turtles[0].x(); }xcor()          { return this.turtles.length == 0? null: this.turtles[0].xcor(); }y()             { return this.turtles.length == 0? null: this.turtles[0].y(); }ycor()          { return this.turtles.length == 0? null: this.turtles[0].ycor(); }set(key, value) { this.turtles.forEach(i => i[key] = value); return this; }get(key) { return this.turtles.length == 0? null: this.turtles[0][key]; }}return new Bale(n, turtleClass);}
function Bales(count, includeFullTransparent = true, turtleClass = null) { if(count == 1) return [new Bale(1, turtleClass)]; const getExponent = (base, target) => Math.log(target) / Math.log(base); const baleSize = count - (includeFullTransparent?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(includeFullTransparent) n.push(0); return n.map(i => new Bale(i, turtleClass));}

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