// LL 2021

// From Wolfram Alpha
// const trajectory = 0 // min=0 max=16 step=1 (Random search,"AMTMNQQXUYGA", "CVQKGHQTPHTE", "FIRCDERRPVLD", "GIIETPIQRRUL", "GLXOESFTTPSV", "GXQSNSKEECTX", "HGUHDPHNSGOH", "ILIBVPKJWGRR", "LUFBBFISGJYS", "MCRBIPOPHTBN", "MDVAIDOYHYEA", "ODGQCNXODNYA", "QFFVSLMJJGCR", "UWACXDQIGKHF", "VBWNBDELYHUL", "WNCSLFLGIHGL")
// const trajectories = [ "", "AMTMNQQXUYGA", "CVQKGHQTPHTE", "FIRCDERRPVLD", "GIIETPIQRRUL", "GLXOESFTTPSV", "GXQSNSKEECTX", "HGUHDPHNSGOH", "ILIBVPKJWGRR", "LUFBBFISGJYS", "MCRBIPOPHTBN", "MDVAIDOYHYEA", "ODGQCNXODNYA", "QFFVSLMJJGCR", "UWACXDQIGKHF", "VBWNBDELYHUL", "WNCSLFLGIHGL" ]

// Random ones
// const trajectory = 0 // min=0 max=10 step=1 (Random search, TURTLETOYvoa, Ewtlmwugutaq, Bitglqlmqyjb, Oaegihulgckd, Ujgiufqoledg, Hiooquqfthee, Thpoiknyvwtd, Gtwlfwqxmbpv, Aklogsxymbkg, Bqrphltsatji)
// const trajectories = [ "", "TURTLETOYvoa", "Ewtlmwugutaq", "Bitglqlmqyjb", "Oaegihulgckd", "Ujgiufqoledg", "Hiooquqfthee", "Thpoiknyvwtd", "Gtwlfwqxmbpv", "Aklogsxymbkg", "Bqrphltsatji" ]

// English words
const trajectory = 0 // min=0 max=32 step=1 (Random search,Mockingbirds,Imprevisible,Unsquirelike,Precipitancy,Nonrectified,Prodigiously,Overhumanity,Tobogganists,Reminiscence,Innoculation,Frustrations,Pseudogaster,Significator,Equidistance,Barometrical,Nonobsession,Unconfidence,Begottenness,Unfavourable,Orthoclastic,Irreprovably,Hexiological,Pinguiferous,Plasmodesmus,Unobtainably,Maleficences,Representant,Kendallville,Unassessable,Reinoculated,Reimbushment,Verificatory)
const trajectories = [ "", "Mockingbirds", "Imprevisible", "Unsquirelike", "Precipitancy", "Nonrectified", "Prodigiously", "Overhumanity", "Tobogganists", "Reminiscence", "Innoculation", "Frustrations", "Pseudogaster", "Significator", "Equidistance", "Barometrical", "Nonobsession", "Unconfidence", "Begottenness", "Unfavourable", "Orthoclastic", "Irreprovably", "Hexiological", "Pinguiferous", "Plasmodesmus", "Unobtainably", "Maleficences", "Representant", "Kendallville", "Unassessable", "Reinoculated", "Reimbushment", "Verificatory" ]

const plottable = 0; // min=0 max=1 step=1 (No,Yes)
Canvas.setpenopacity(plottable?1:-0.25)
// MOCKINGBIRDS, IMPREVISIBLE, NONRECTIFIED, PRECIPITANCY, UNSQUIRELIKE, PRODIGIOUSLY, OVERHUMANITY, TOBOGGANISTS, REMINISCENCE, INNOCULATION, FRUSTRATIONS, PSEUDOGASTER, SIGNIFICATOR, EQUIDISTANCE, BAROMETRICAL, NONOBSESSION, UNCONFIDENCE, BEGOTTENNESS, UNFAVOURABLE, ORTHOCLASTIC, IRREPROVABLY, HEXIOLOGICAL, PINGUIFEROUS, PLASMODESMUS, UNOBTAINABLY, MALEFICENCES, REPRESENTANT, KENDALLVILLE, UNASSESSABLE, REINOCULATED, REIMBUSHMENT, VERIFICATORY
turtle = plottable ? new Slowpoke() : new Turtle(), a = []
redo = rewind = 0, newTrajectory(), init_iterations = 100000
function walk(ii) {
    const nx = a[0] + a[1] * x + a[2] * x**2 + a[3] * x * y + a[4]  * y + a[5]  * y**2
    const ny = a[6] + a[7] * x + a[8] * x**2 + a[9] * x * y + a[10] * y + a[11] * y**2
    x = nx, y = ny, i = ii - rewind
    if (i < init_iterations * 0.99 && (isNaN(x) || Math.abs(x) > 10 || isNaN(y) || Math.abs(y) > 10)) newTrajectory(ii)
    if (isNaN(x) || Math.abs(x) > 10 || isNaN(y) || Math.abs(y) > 10) newTrajectory(ii);
    if (i < init_iterations && x == nx && y == ny) {
        addToBins(ii)
        min_x = Math.min(min_x, x), max_x = Math.max(max_x, x)
        min_y = Math.min(min_y, y), max_y = Math.max(max_y, y)
    } else if (i == init_iterations) {
        x = y = 0
        if ((max_x - min_x) > (max_y - min_y)) { const cc = (min_y + max_y) / 2, dd = (max_x - min_x) / 2; min_y = cc - dd, max_y = cc + dd }
        else { const cc = (min_x + max_x) / 2, dd = (max_y - min_y) / 2; min_x = cc - dd, max_x = cc + dd }
        console.log(`setup: ${setup} - attempts: ${redo} - x: [${min_x.toFixed(2)},${max_x.toFixed(2)}] - y: [${min_y.toFixed(2)},${max_y.toFixed(2)}]`)
    } else if (x == nx && y == ny) {
        const bx = ((x - min_x) / (max_x - min_x) - 0.5) * 190, by = ((max_y - y) / (max_y - min_y) - 0.5) * 190
        turtle.jump(bx, by), turtle.forward(plottable?0.5:0.1)
    }
    if (i < 1<<(plottable?18:21)) return true
	if (plottable) console.log(`Slowpoke: draw: ${slowpoke_draw}, skip: ${slowpoke_skip}`)
	return false
}
function newTrajectory(rw=0) { 
    if (typeof word_list !== 'undefined' && word_list.length > 0) setup = word_list[Math.random() * word_list.length | 0].toUpperCase();
    else setup = "" + trajectories[trajectory].toUpperCase()
    min_x = min_y = Number.MAX_VALUE, max_x = max_y = -Number.MAX_VALUE, x = y = 0, redo++, bins = {}
    if (rewind < 1 << 15) rewind=rw
    while (setup.length < 12) r = Math.random() * 25 | 0, setup += String.fromCharCode(r + 65)
    for (var j=0; j<12; j++) {
        a[j] = (setup.charCodeAt(j) - 65) * 0.1 - 1.2
        if (Math.abs(a[j]) > 1.21) r = Math.random() * 25 | 0, a[j] = r * 0.1 - 1.2, setup = setup.substring(0, j) + String.fromCharCode(r + 65) + setup.substring(j + 1)
    }
}
function addToBins(ii) {
    mx = (x - min_x) / (max_x - min_x), my = (y - min_y) / (max_y - min_y)
    key = '' + mx.toFixed(2)+';'+my.toFixed(2);
    if (key in bins) bins[key]++; else bins[key] = 1
    if (bins[key] > 10000) newTrajectory(ii)
}

////////////////////////////////////////////////////////////////
// Slowpoke utility code. Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/cfe9091ad8
////////////////////////////////////////////////////////////////
function Slowpoke(o,e){const t={};return new class extends Turtle{goto(o,e){const s=Array.isArray(o)?[...o]:[o,e];if(this.isdown()){const o=[this.x(),this.y()],e=0,i=1,r=o[0].toFixed(e)+"_"+s[0].toFixed(e)+o[1].toFixed(i)+"_"+s[1].toFixed(i),d=s[0].toFixed(e)+"_"+o[0].toFixed(e)+s[1].toFixed(i)+"_"+o[1].toFixed(i);if(t[r]||t[d])return super.up(),super.goto(s),super.down(),void slowpoke_skip++;t[r]=t[d]=!0,slowpoke_draw++}super.goto(s)}}(o,e)}var slowpoke_skip=0,slowpoke_draw=0;

// Optional word list to guide the search
//word_list = []