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number_wall.html
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number_wall.html
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<!DOCTYPE html>
<html>
<head>
<title>Number Wall</title>
<link rel="icon" href="res/favicon.ico">
<script type="text/javascript">
/*
a
bcd
o
bd + ao = c2
o = (c2 - bd) / a
When a is 0:
e
f
gh0ij
c
o
gi2 + h2j = ec2 + f2o
o = (gi2 + h2j - ec2) / f2
When f is also 0, 0s will form a square:
yyyy
xxxxxx
yx0000xy
yx0000xy
yx0000xy
yx0000xy
xaaaax
bbbb
Calculate a's from x's:
x > X > x
v ^
Y Z
v ^
x > A > x
All 4 sides of the square will form a geometric sequence. Multipliers (X,Y,Z,A)
are all rational, and related like this:
YZ = XA A = YZ/X if square of 0s has an even size
YZ = -XA A = -YZ/X if square of 0s has an odd size
Calculate b's using x's, y's, and a's, and the multipliers from before:
f>
e>
hg0000
vv0000
0000^^
0000cd
<a
<b
Yf/e - Xh/g = Zb/a - Ad/c
b = (Yf/e - Xh/g + Ad/c)a/Z
*/
let wallWidth = 30;
let wallHeight = 30;
let wall = null;
let testMode = false;
let domWall = null;
let domColorMod = null;
let domColorModVal = null;
let domSeqSel = null;
let domRecur = null;
let domRecurFormula = null;
let domRecurVals = null;
let domNoRecur = null;
let domCustom = null;
function safeBigInt(x) {
try {
return BigInt(x);
} catch (e) {}
return null;
}
function safeGet(node, defaultValue = null) {
return safeBigInt(node.value) ?? defaultValue;
}
function clamp(x, lo, hi) {
return x <= lo ? lo : (x >= hi ? hi : x);
}
function lerp(x0, x1, k) {
return x0 * (1 - k) + x1 * k;
}
function gcd(a, b) {
if (a < b) return gcd(b, a);
while (b > 0) {
const c = a % b;
a = b;
b = c;
}
return a;
}
function genSeed() {
let x = 0n;
for (let i = 0; i < 16; ++i) {
x <<= 8n;
x |= BigInt(~~(0x100 * Math.random()));
}
return x;
}
class Random {
constructor(seed = null) {
this.x = BigInt(seed ?? genSeed());
}
rand() {
const r = Number(this.x & 0xFFFFFFFFn);
for (let i = 0; i < 32; ++i) {
const b = (this.x >> 128n) ^ (this.x >> 126n) ^ (this.x >> 101n) ^
(this.x >> 99n);
this.x = (this.x >> 1n) | ((b & 1n) << 127n);
}
return r / (1 << 16) / (1 << 16);
}
randf(h = 1, l = 0) {
return l + this.rand() * (h - l);
}
randi(h = 1, l = 0) {
return Math.floor(this.randf(h + 1, l));
}
}
class Frac {
constructor(u, v, skipReduction = false) {
console.assert(v != 0, u, v);
if (u == 0) {
this.u = 0n;
this.v = 1n;
return;
}
this.u = BigInt(v < 0 ? -u : u);
this.v = BigInt(v < 0 ? -v : v);
if (!skipReduction) this.reduce();
}
reduce() {
const negative = this.u < 0;
const u = negative ? -this.u : this.u;
const w = gcd(u, this.v);
this.u = (negative ? -u : u) / w;
this.v = this.v / w;
}
mul(o) {
// Assuming this and o are already reduced, the only reducing that needs to
// happen looks like (ab/c)*(d/ae), which we can do like (d/c)*(ab/ae).
// This is a win because (ab/ae) is faster to reduce than (adb/ace), as it
// lets us reduce before we multiply.
const x = new Frac(this.u, o.v);
const y = new Frac(o.u, this.v);
return new Frac(x.u * y.u, x.v * y.v, true);
}
add(o) {
// If the denominators of this and o are ax and ay, then the new denominator
// can be axy, with the numerators being multiplied by y and x respectively.
// We still have to reduce the final fraction, but this saves a bit of work.
const z = new Frac(this.v, o.v);
return new Frac(this.u * z.v + o.u * z.u, this.v * z.v);
}
neg() { return new Frac(-this.u, this.v, true); }
abs() { return this.isNeg() ? this.neg() : this; }
inv() { return new Frac(this.v, this.u, true); }
div(o) { return this.mul(o.inv()); }
sub(o) { return this.add(o.neg()); }
equals(o) { return this.u == o.u && this.v == o.v; }
isZero() { return this.u == 0; }
isOne() { return this.u == this.v; }
isNeg() { return this.u < 0; }
isFrac() { return true; }
isInt() { return this.v == 1; }
intMul(x) {
const ux = x * this.u;
console.assert(ux % this.v == 0, this, x);
return ux / this.v;
}
intMod(n) {
const nv = this.v * n;
return new Frac(((this.u % nv) + nv) % nv, this.v, true);
}
toInt() {
console.assert(this.v == 1, this.u, this.v);
return this.u;
}
toNum() {
return Number(this.u) / Number(this.v);
}
toString() {
let s = '' + this.u;
if (this.v != 1) s += '/' + this.v;
return s;
}
}
class Polynomial {
constructor(coeffs) {
this.a = coeffs;
console.assert(this.a.every((e) => e.isFrac()));
while (this.a.length > 0 && this.a[this.a.length - 1].isZero()) {
this.a.pop();
}
}
mul(o) {
const b = [];
for (let i = 0; i < this.a.length; ++i) {
for (let j = 0; j < o.a.length; ++j) {
const k = i + j;
const y = this.a[i].mul(o.a[j]);
if (k >= b.length) {
console.assert(k == b.length);
b.push(y);
} else {
b[k] = b[k].add(y);
}
}
}
return new Polynomial(b);
}
add(o) {
const b = [];
const an = this.a.length;
const on = o.a.length;
const n = an > on ? an : on;
for (let i = 0; i < n; ++i) {
b.push(i < an ? (i < on ? this.a[i].add(o.a[i]) : this.a[i]) : o.a[i]);
}
return new Polynomial(b);
}
toFrac() {
console.assert(this.a.length <= 1);
return this.a.length == 0 ? new Frac(0n, 1n, true) : this.a[0];
}
toInt() { return this.toFrac().toInt(); }
degree() { return this.a.length == 0 ? 0 : this.a.length - 1; }
term(i) { return i < this.a.length ? this.a[i] : 0; }
isZero() { return this.a.length == 0; }
sub(o) { return this.add(o.neg()); }
neg() { return new Polynomial(this.a.map(f => f.neg())); }
isPoly() { return true; }
equals(o) {
if (this.a.length != o.a.length) return false;
for (let i = 0; i < this.a.length; ++i) {
if (!this.a[i].equals(o.a[i])) return false;
}
return true;
}
divExpectFrac(o) {
// Divide by a polynomial. Expect a simple fraction result.
console.assert(o.isPoly());
console.assert(!o.isZero());
if (this.isZero()) return this;
console.assert(this.a.length == o.a.length);
const y = this.a[0].div(o.a[0]);
if (testMode) {
for (let i = 1; i < this.a.length; ++i) {
const z = this.a[i].div(o.a[i]);
console.assert(y.equals(z));
}
}
return y;
}
divExpectPoly(o) {
// Divide by a polynomial. Expect a polynomial result.
console.assert(o.isPoly());
console.assert(!o.isZero());
if (this.isZero()) return this;
const q = this.a.map(e => new Frac(0, 1));
const r = this.a.slice();
// Maintain the invariant that o * q + r == this.
const rlen = () => {
for (let i = r.length - 1; i >= 0; --i) {
if (!r[i].isZero()) return i + 1;
}
return 0;
};
const on = o.a.length - 1;
const oc = o.a[on];
while (rlen() >= o.a.length) {
const rn = rlen() - 1;
const t = r[rn].div(oc);
const tn = rn - on;
console.assert(tn >= 0);
q[tn] = q[tn].add(t);
for (let i = 0; i <= on; ++i) {
const m = t.mul(o.a[i]);
const mn = i + tn;
console.assert(mn < r.length);
r[mn] = r[mn].sub(m);
}
}
console.assert(rlen() == 0);
return new Polynomial(q);
}
fracDiv(o) {
// Divide by a fraction.
console.assert(o.isFrac());
return new Polynomial(this.a.map(f => f.div(o)));
}
fracMul(o) {
// Multiply by a fraction.
console.assert(o.isFrac());
return new Polynomial(this.a.map(f => f.mul(o)));
}
toString() {
if (this.a.length == 0) return '0';
let s = '';
for (let i = this.a.length - 1; i >= 0; --i) {
let f = this.a[i];
if (f.isZero()) continue;
if (s.length > 0) {
s += f.isNeg() ? ' - ' : ' + ';
f = f.abs();
}
if (i == 0 || !f.isOne()) s += f.toString();
if (i > 0) s += 'x';
if (i > 1) s += '^' + i;
}
return s;
}
toRecurrenceString(rn) {
if (this.a.length == 0) return '0';
let s = '';
for (let i = this.a.length - 1; i >= 0; --i) {
let f = this.a[i];
if (f.isZero()) continue;
if (s.length > 0) {
s += f.isNeg() ? ' - ' : ' + ';
f = f.abs();
}
if (!f.isOne()) s += f.toString();
s += 'Sn-' + (rn - i);
}
return s;
}
applyRecurrence(seq, rn, from, to) {
const o = [];
const s = (i) => i < from ? seq(i) : o[i - from];
for (let i = from; i < to; ++i) {
let y = 0;
for (let j = 0; j < rn; ++j) {
y += this.term(rn - 1 - j) * s(i - 1 - j);
}
o.push(y);
}
return o;
}
}
function intToPoly(x0) {
return new Polynomial([new Frac(BigInt(x0), 1)]);
}
function linearPoly(x0, x1) {
return new Polynomial([new Frac(BigInt(x0), 1), new Frac(BigInt(x1), 1)]);
}
function fracToPoly(f) {
console.assert(f.isFrac());
return new Polynomial([f]);
}
function cache1D(fn) {
const cache = new Map();
return (i) => {
if (!cache.has(i)) cache.set(i, fn(i));
return cache.get(i);
};
}
function cache2D(fn) {
const cache = new Map();
return (ri, ci) => {
if (!cache.has(ri)) cache.set(ri, new Map());
const row = cache.get(ri);
if (!row.has(ci)) row.set(ci, fn(ri, ci));
return row.get(ci);
};
}
class Window {
constructor(boundUp = false, boundLeft = false, boundRight = false) {
this.rlo = null;
this.rhi = null;
this.clo = null;
this.chi = null;
this.x = null;
this.y = null;
this.z = null;
this.a = null;
this.boundUp = boundUp;
this.boundDown = false;
this.boundLeft = boundLeft;
this.boundRight = boundRight;
}
minSize() {
return Math.max(this.rhi - this.rlo, this.chi - this.clo);
}
updateBounds() {
const s = this.minSize();
if (this.boundUp) this.rhi = this.rlo + s;
if (this.boundDown) this.rlo = this.rhi - s;
if (this.boundLeft) this.chi = this.clo + s;
if (this.boundRight) this.clo = this.chi - s;
if (this.boundLeft && this.boundRight) {
this.boundUp = this.boundDown = (this.boundUp || this.boundDown);
}
if (this.boundUp && this.boundDown) {
this.boundLeft = this.boundRight = (this.boundLeft || this.boundRight);
}
}
add(ri, ci) {
if (this.rlo == null || ri < this.rlo) this.rlo = ri;
if (this.rhi == null || ri > this.rhi) this.rhi = ri;
if (this.clo == null || ci < this.clo) this.clo = ci;
if (this.chi == null || ci > this.chi) this.chi = ci;
this.updateBounds();
}
isInside(ri, ci) {
if (ri >= this.rlo && ri <= this.rhi &&
ci >= this.clo && ci <= this.chi) {
return 1; // Definitely inside.
}
if (this.boundLeft && this.boundRight && this.boundUp && this.boundDown) {
return 0; // Definitely outside.
}
return -1; // Unknown.
}
expandHorizontally(cellFn) {
console.assert(!this.boundLeft || !this.boundRight);
const expandRight = this.boundLeft;
const ciexp = expandRight ? this.chi + 1 : this.clo - 1;
if (cellFn(this.rlo, ciexp) == 0) {
this.add(this.rlo, ciexp);
} else {
if (expandRight) {
this.boundRight = true;
} else {
this.boundLeft = true;
}
this.updateBounds();
}
}
toString(cellFn) {
let s = `(${this.rlo}, ${this.clo}) -> (${this.rhi}, ${this.chi})\n`;
for (let ri = this.rlo - 2; ri <= this.rhi + 2; ++ri) {
for (let ci = this.clo - 2; ci <= this.chi + 2; ++ci) {
if (ri <= this.rhi) {
s += cellFn(ri, ci).toString();
} else if (ci >= this.clo && ci <= this.chi) {
s += '?';
} else if (
ri == this.rhi + 1 && (ci == this.clo - 1 || ci == this.chi + 1)) {
s += cellFn(ri, ci).toString();
} else {
s += ' ';
}
s += '\t';
}
s += '\n';
}
return s;
}
fillMultipliers(cellFn) {
console.assert(
this.boundLeft && this.boundRight && this.boundUp && this.boundDown);
if (this.a != null) return;
const fn = (rlo, clo, rhi, chi, dr, dc) => {
let m = null;
let r = rlo;
let c = clo;
let v = cellFn(r, c);
while (true) {
const nr = r + dr;
const nc = c + dc;
const nv = cellFn(nr, nc);
const nm = nv.divExpectFrac(v);
if (m == null) {
m = nm;
if (!testMode) break;
} else {
console.assert(m.equals(nm), m, nm);
}
r = nr;
c = nc;
v = nv;
if (r == rhi && c == chi) break;
}
return m;
};
this.x = fn(this.rlo - 1, this.clo - 1, this.rlo - 1, this.chi + 1, 0, 1);
this.y = fn(this.rlo - 1, this.clo - 1, this.rhi + 1, this.clo - 1, 1, 0);
this.z = fn(this.rhi + 1, this.chi + 1, this.rlo - 1, this.chi + 1, -1, 0);
this.a = this.y.mul(this.z).div(this.x);
if (this.minSize() % 2 == 1) this.a = this.a.neg();
}
horseshoeRule(ri, ci, cellFn) {
console.assert(
this.boundLeft && this.boundRight && this.boundUp && this.boundDown);
this.fillMultipliers(cellFn);
if (ri == this.rhi + 1) {
return cellFn(ri, ci - 1).fracMul(this.a);
} else {
console.assert(ri == this.rhi + 2);
const dc = this.chi - ci;
const a = cellFn(this.rhi + 1, this.chi - dc);
const c = cellFn(this.rhi - dc, this.chi + 1);
const d = cellFn(this.rhi - dc, this.chi + 2);
const e = cellFn(this.rlo - 1, this.clo + dc);
const f = cellFn(this.rlo - 2, this.clo + dc);
const g = cellFn(this.rlo + dc, this.clo - 1);
const h = cellFn(this.rlo + dc, this.clo - 2);
return (
f.fracMul(this.y).divExpectPoly(e).sub(
h.fracMul(this.x).divExpectPoly(g)).add(
d.fracMul(this.a).divExpectPoly(c))
).mul(a).fracDiv(this.z);
}
}
}
function makeWallGenerator(inputRowFn) {
let cellFn = null, winFn = null;
const firstWinInColumn = new Map();
const upperWin = new Window();
const winFnInner = (ri, ci) => {
// We want to walk to find the upper right corner of the window. But it's
// possible that this is a lower infinite window. So first, walk up until
// we find the top edge of the window.
const winUp = winFn(ri - 1, ci);
if (winUp != null) return winUp;
// Next, check if there are any known windows on this row, so that we can
// dedupe with them.
if (!firstWinInColumn.has(ri)) {
// This is the first window on this row, so start a new window.
return new Window(true);
}
// Walk towards that window (could be to our left or right). If we hit a
// wall, this is a seperate window. If we hit a window, dedupe with it.
const dc = firstWinInColumn.get(ri) < ci ? -1 : 1;
const winLr = winFn(ri, ci + dc);
if (winLr != null) return winLr;
// The cell in the direction of the first window is a wall. So start a
// new window.
return new Window(true, dc == -1, dc == 1);
};
winFn = cache2D((ri, ci) => {
// console.log('winFn', ri, ci);
// The upper window is infinite, so need to special case it.
if (ri <= -3) return upperWin;
// Check that this is actually a window cell.
if (!cellFn(ri, ci).isZero()) return null;
// Main window hunting logic.
const win = winFnInner(ri, ci);
win.add(ri, ci);
// Update the firstWinInColumn.
if (!firstWinInColumn.has(ri)) firstWinInColumn.set(ri, ci);
return win;
});
const cellFnInner = (ri, ci) => {
if (ri <= -3) return intToPoly(0n);
if (ri == -2) return intToPoly(1n);
if (ri == -1) return inputRowFn(ci);
const a = cellFn(ri - 2, ci);
const c = cellFn(ri - 1, ci);
if (!a.isZero()) {
// Cross rule.
const b = cellFn(ri - 1, ci - 1);
const d = cellFn(ri - 1, ci + 1);
return (c.mul(c).sub(b.mul(d))).divExpectPoly(a);
}
const f = cellFn(ri - 3, ci);
if (!f.isZero()) {
// Long cross rule.
const e = cellFn(ri - 4, ci);
const g = cellFn(ri - 2, ci - 2);
const h = cellFn(ri - 2, ci - 1);
const i = cellFn(ri - 2, ci + 1);
const j = cellFn(ri - 2, ci + 2);
return (g.mul(i).mul(i).add(
h.mul(h).mul(j)).sub(
e.mul(c).mul(c))
).divExpectPoly(f.mul(f));
}
// Find the window that a and f are in.
const win = winFn(ri - 2, ci);
console.assert(win != null);
console.assert(win != upperWin);
console.assert(win == winFn(ri - 2, ci));
console.assert(win.boundUp);
while (true) {
// Are we inside the window? If so, return 0.
const inside = win.isInside(ri, ci);
if (inside == 1) return intToPoly(0n);
if (inside == 0) break;
// If we don't know yet, expand the window left or right.
win.expandHorizontally(cellFn);
}
// Horseshoe rule.
return win.horseshoeRule(ri, ci, cellFn);
};
cellFn = cache2D((ri, ci) => {
const val = cellFnInner(ri, ci);
// console.log('cellFn', ri, ci, val.toString());
return val;
});
return cellFn;
}
function newElement(type, parent, classes = [], text = null) {
const n = document.createElement(type);
if (text != null) n.innerText = text;
for (const cls of classes) n.classList.add(cls);
if (parent != null) parent.appendChild(n);
return n;
}
function newDiv(parent, classes = [], text = null) {
return newElement('div', parent, classes, text);
}
function newTextEdit(parent, classes = [], initValue = null) {
const n = newElement('input', parent, classes);
n.type = 'text';
n.value = initValue;
return n;
}
function emptyDiv(n) {
while (n.hasChildNodes()) n.removeChild(n.lastChild);
}
let fibGenerator = null;
fibGenerator = cache1D((i) => {
if (i == 0) return 0;
if (i == 1) return 1;
if (i > 0) return fibGenerator(i - 1) + fibGenerator(i - 2);
return fibGenerator(i + 2) - fibGenerator(i + 1);
});
function squareGenerator(i) { return i * i; }
function cubeGenerator(i) { return i * i * i; }
function pow2Generator(i) { return 1n << BigInt(Math.abs(i)); }
function pagodaImpl(n) { return (n & ((n & -n) << 1)) ? 1 : 0; }
function pagodaGenerator(n) { return pagodaImpl(n + 1) - pagodaImpl(n - 1); }
class RandomSequence {
constructor() {
this.rand = new Random();
this.seq = [];
}
get(i) {
const j = i >= 0 ? 2 * i : -2 * i - 1;
while (j >= this.seq.length) this.seq.push(this.rand.randi(10, -10));
return this.seq[j];
}
}
function customGenerator(eqn) {
const fn = new Function('n', `return ${eqn};`);
return (i) => fn(i);
}
const randSeq = new RandomSequence();
function getSequenceGenerator() {
if (domSeqSel.value == 'Custom') {
domCustom.classList.remove('hidden');
return customGenerator(domCustom.value);
}
domCustom.classList.add('hidden');
if (domSeqSel.value == 'Fibonacci') return fibGenerator;
if (domSeqSel.value == 'Squares') return squareGenerator;
if (domSeqSel.value == 'Cubes') return cubeGenerator;
if (domSeqSel.value == 'Pow2') return pow2Generator;
if (domSeqSel.value == 'Pagoda') return pagodaGenerator;
if (domSeqSel.value == 'Random') return (i) => randSeq.get(i);
if (domSeqSel.value == 'Zeros') return (i) => 0;
}
const gradient = [
[0, 0, 0],
[94, 53, 177],
[233, 30, 99],
[255, 87, 34],
[255, 193, 7],
[255, 241, 118],
];
function modColorGradient(x) {
const y = x * (gradient.length - 1);
const i = clamp(Math.floor(y), 0, gradient.length - 1);
const j = clamp(i + 1, 0, gradient.length - 1);
const f = y - i;
const r = lerp(gradient[i][0], gradient[j][0], f);
const g = lerp(gradient[i][1], gradient[j][1], f);
const b = lerp(gradient[i][2], gradient[j][2], f);
return `rgb(${r}, ${g}, ${b})`;
}
let userInputs = [];
function buildWall(inputs) {
if (inputs == null) {
inputs = userInputs = [];
}
emptyDiv(domWall);
const withInputs = (fn) => (i) => safeBigInt(inputs[i]) ?? fn(i);
const sequenceGenerator = withInputs(getSequenceGenerator());
const clrMod = safeGet(domColorMod, 1n);
domColorModVal.innerText = clrMod == 1 ? 'Off' : clrMod;
if (clrMod > 1) {
domWall.classList.add('colorModEnabled');
} else {
domWall.classList.remove('colorModEnabled');
}
const inputConv = (fn) => (i) => intToPoly(fn(i));
const wallGen = makeWallGenerator(inputConv(sequenceGenerator));
const wallVals = [];
for (let ri = -1; ri < wallHeight; ++ri) {
const row = [];
for (let ci = 0; ci < wallWidth; ++ci) {
row.push(wallGen(ri, ci).toFrac());
}
wallVals.push(row);
}
// Truncate the wall so there's only one all-zero row at the end.
let finalWallRow = wallHeight;
for (let rip1 = wallVals.length - 1; rip1 >= 1; --rip1) {
if (!wallVals[rip1].every((e) => e.isZero())) break;
if (rip1 + 1 < wallVals.length) {
console.assert(rip1 + 2 == wallVals.length);
wallVals.pop();
finalWallRow = rip1 - 2;
}
}
for (let rip1 = 0; rip1 < wallVals.length; ++rip1) {
const row = newDiv(domWall, ['row']);
for (let ci = 0; ci < wallWidth; ++ci) {
const val = wallVals[rip1][ci];
const str = val.toString();
const isBig = str.length > 3;
const shownVal = isBig ? 'big' : str;
if (rip1 == 0) {
const cell = newTextEdit(row, ['cell', 'in'], str);
cell.addEventListener('change', () => {
userInputs[ci] = safeGet(cell);
buildWall(userInputs);
});
} else {
const cell = newDiv(row, ['cell', 'out'], shownVal);
cell.title = str;
if (clrMod > 1) {
const modVal = Number(val.intMod(clrMod).toNum()) / Number(clrMod);
cell.style.backgroundColor = modColorGradient(modVal);
}
}
}
}
if (finalWallRow == wallHeight) {
domRecur.classList.add('hidden');
domNoRecur.classList.remove('hidden');
} else {
// Run the wall generator using polynomial inputs, to get the recurrence.
const polyInputConv = (fn) => (i) => linearPoly(fn(i), -fn(i - 1));
const wallPolyGen = makeWallGenerator(polyInputConv(sequenceGenerator));
// The recurrence polynomial is any element of the final row. Choose the
// cell on the diagonal, so that we avoid cells off the edge of the grid.
const recurrence = wallPolyGen(finalWallRow, finalWallRow);
const rn = recurrence.degree();
const r2 = recurrence.isZero() ? recurrence : new Polynomial(
recurrence.a.slice(0, rn)).fracDiv(recurrence.term(rn).neg());
domRecur.classList.remove('hidden');
domNoRecur.classList.add('hidden');
domRecurFormula.innerText = 'Sn = ' + r2.toRecurrenceString(rn);
domRecurVals.innerText = r2.applyRecurrence(
sequenceGenerator, rn, wallWidth, wallWidth + 8).join(', ');
}
}
function growWall(dr, dc) {
wallHeight = clamp(wallHeight + dr, 1, 100);
wallWidth = clamp(wallWidth + dc, 1, 100);
buildWall(userInputs);
}
function onLoad() {
domWall = document.getElementById('wall');
domColorMod = document.getElementById('colorMod');
domColorModVal = document.getElementById('colorModVal');
domSeqSel = document.getElementById('sequenceSelect');
domRecur = document.getElementById('recur');
domRecurFormula = document.getElementById('recurFormula');
domRecurVals = document.getElementById('recurVals');
domNoRecur = document.getElementById('noRecur');
domCustom = document.getElementById('custom');
buildWall(null);
domColorMod.addEventListener('change', () => buildWall(userInputs));
domSeqSel.addEventListener('change', () => buildWall(null));
domCustom.addEventListener('change', () => buildWall(userInputs));
}
window.addEventListener('load', onLoad);
</script>
<style>
body {
background-color: #212121;
margin: 0;
}
#head {
background-color: #424242;
width: 100%;
display: flex;
justify-content: space-around;
margin-bottom: 16px;
}
h1, #index {
color: #ffc107;
text-align: center;
font-family: monospace;
font-size: 42px;
flex-grow: 1;
padding: 16px;
margin: 0;
}
#index {
color: #ff5722;
text-decoration: none;
flex-grow: 0;
}
h2 {
color: #ff5722;
font-family: monospace;
}
a {
color: #ffc107;
font-family: monospace;
font-size: 16px;
cursor: pointer;
text-decoration: underline;
}
#wrap {
padding: 0 16px;
color: #f5f5f5;
font-family: monospace;
font-size: 16px;
display: flex;
flex-direction: row;
gap: 16px;
}
#left {
max-width: 400px;
width: 25%;
}
#right {
flex-grow: 1;
display: flex;
justify-content: space-around;
}
.shh {
opacity: 15%;
}
#wall {
display: flex;
flex-direction: column;
border-top: 1px solid #424242;
}
.row {
height: 24px;
display: flex;
border-right: 1px solid #424242;
}
.cell {
width: 32px;
padding: 1px;
border-bottom: 1px solid #424242;
border-left: 1px solid #424242;
border-top: 0;
border-right: 0;
}
.colorModEnabled .cell.out {
color: #aaaaaa66;
}
.hidden {
display: none;
}
#recurFormula {
color: #8bc34a;
}
#recurVals {
color: #2196f3;
}
.button {
color: #ffc107;
cursor: pointer;
user-select: none;
}
</style>
</head>
<body>
<div id="head">
<a id="index" href="index.html"><</a>
<h1>Number Wall</h1>
</div>
<div id="wrap">
<div id="left">
Number walls are a tool for analyzing integer sequences. The sequence is
input into the top row, and the other rows of numbers are calculated
according to the cross rule (by solving for D):<br/><br/>
<img src="res/cross_rule.svg"/><br/><br/>
There are other more elaborate rules for cases where zeros make the cross
rule useless (when C is 0). For more details, see this
<a href="https://youtu.be/NO1_-qptr6c">Mathologer video</a>.<br/><br/>
UI note: For numbers that don't fit, I just write "big", but you can hover
over the cell to see the actual value.<br/><br/>
Sequence:
<select id="sequenceSelect">
<option value="Fibonacci">Fibonacci</option>
<option value="Squares">Squares</option>
<option value="Cubes">Cubes</option>
<option value="Pagoda">Pagoda</option>
<option value="Random">Random</option>
<option value="Custom">Custom JS</option>
</select>
<input type="text" id="custom" value="n ^ 4"/>
<br/><br/>
Color modulo:
<span id="colorModVal">Off</span>
<input type="range" id="colorMod" min="1" max="10" value="1"/>
<br/><br/>
Grow/shrink wall:
<span class="button" onclick="growWall(-1, 0)">🡅</span>