September 2017 Update
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Ingy döt Net
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14570 changed files with 153136 additions and 63871 deletions
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// A Sierpinski triangle of order N,
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// constructed as 2^N lines of Pascal's triangle mod 2
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// and mapped to centred {1:asterisk, 0:space} strings
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(() => {
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'use strict';
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(order => {
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// LINES OF SIERPINSKI TRIANGLE AT LEVEL N -------------------------------
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// sierpinski :: Int -> [Bool]
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let sierpinski = intOrder => {
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// sierpinski :: Int -> [String]
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const sierpTriangle = n =>
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// Previous triangle centered with left and right padding,
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(n > 0) ? concat(ap([
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map(xs => intercalate(xs, ap(
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[s => concat(replicate(Math.pow(2, (n - 1)), s))], [' ', '-']
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))),
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// asciiPascalMod2 :: Int -> [[Int]]
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let asciiPascalMod2 = nRows =>
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range(1, nRows - 1)
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.reduce(sofar => {
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let lstPrev = sofar.slice(-1)[0];
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// above a pair of duplicates, placed one character apart.
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map(xs => intercalate('+', [xs, xs]))
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], [sierpTriangle(n - 1)])) : ['▲'];
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// The composition of (asciiBinary . mod 2 . add)
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// is reduced here to a rule from two parent characters
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// to a single child character.
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// Rule 90 also reduces to the same XOR
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// relationship between left and right neighbours.
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// GENERIC FUNCTIONS -----------------------------------------------------
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return sofar
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.concat([zipWith(
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(left, right) => left === right ? ' ' : '*',
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[' '].concat(lstPrev),
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lstPrev.concat(' ')
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)]);
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}, [
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['*'] // Tip of triangle
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]);
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// Reduce/folding from the last item (base of list)
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// which has zero left indent.
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// Each preceding row has one more indent space than the row beneath it
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return asciiPascalMod2(Math.pow(2, intOrder))
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.reduceRight((a, x) => {
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return {
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triangle: a.indent + x.join(' ') + '\n' + a.triangle,
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indent: a.indent + ' '
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}
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}, {
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triangle: '',
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indent: ''
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}).triangle
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// replicate :: Int -> a -> [a]
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const replicate = (n, a) => {
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let v = [a],
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o = [];
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if (n < 1) return o;
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while (n > 1) {
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if (n & 1) o = o.concat(v);
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n >>= 1;
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v = v.concat(v);
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}
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return o.concat(v);
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};
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// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
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let zipWith = (f, xs, ys) =>
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xs.length === ys.length ? (
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xs.map((x, i) => f(x, ys[i]))
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) : undefined,
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// curry :: ((a, b) -> c) -> a -> b -> c
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const curry = f => a => b => f(a, b);
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// range(intFrom, intTo, optional intStep)
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// Int -> Int -> Maybe Int -> [Int]
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range = (m, n, step) => {
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let d = (step || 1) * (n >= m ? 1 : -1);
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// map :: (a -> b) -> [a] -> [b]
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const map = curry((f, xs) => xs.map(f));
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return Array.from({
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length: Math.floor((n - m) / d) + 1
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}, (_, i) => m + (i * d));
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};
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// Apply a list of functions to a list of arguments
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// <*> :: [(a -> b)] -> [a] -> [b]
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const ap = (fs, xs) => //
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[].concat.apply([], fs.map(f => //
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[].concat.apply([], xs.map(x => [f(x)]))));
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return sierpinski(order);
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// unlines :: [String] -> String
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const unlines = xs => xs.join('\n');
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})(4);
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// intercalate :: String -> [a] -> String
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const intercalate = (s, xs) => xs.join(s);
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// concat :: [[a]] -> [a] || [String] -> String
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const concat = xs => {
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if (xs.length > 0) {
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const unit = typeof xs[0] === 'string' ? '' : [];
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return unit.concat.apply(unit, xs);
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} else return [];
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};
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// TEST ------------------------------------------------------------------
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return unlines(sierpTriangle(4));
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})();
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62
Task/Sierpinski-triangle/JavaScript/sierpinski-triangle-4.js
Normal file
62
Task/Sierpinski-triangle/JavaScript/sierpinski-triangle-4.js
Normal file
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@ -0,0 +1,62 @@
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(order => {
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// sierpinski :: Int -> [Bool]
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let sierpinski = intOrder => {
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// asciiPascalMod2 :: Int -> [[Int]]
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let asciiPascalMod2 = nRows =>
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range(1, nRows - 1)
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.reduce(sofar => {
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let lstPrev = sofar.slice(-1)[0];
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// The composition of (asciiBinary . mod 2 . add)
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// is reduced here to a rule from two parent characters
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// to a single child character.
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// Rule 90 also reduces to the same XOR
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// relationship between left and right neighbours.
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return sofar
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.concat([zipWith(
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(left, right) => left === right ? ' ' : '*',
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[' '].concat(lstPrev),
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lstPrev.concat(' ')
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)]);
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}, [
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['*'] // Tip of triangle
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]);
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// Reduce/folding from the last item (base of list)
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// which has zero left indent.
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// Each preceding row has one more indent space than the row beneath it
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return asciiPascalMod2(Math.pow(2, intOrder))
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.reduceRight((a, x) => {
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return {
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triangle: a.indent + x.join(' ') + '\n' + a.triangle,
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indent: a.indent + ' '
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}
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}, {
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triangle: '',
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indent: ''
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}).triangle
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};
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// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
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let zipWith = (f, xs, ys) =>
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xs.length === ys.length ? (
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xs.map((x, i) => f(x, ys[i]))
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) : undefined,
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// range(intFrom, intTo, optional intStep)
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// Int -> Int -> Maybe Int -> [Int]
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range = (m, n, step) => {
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let d = (step || 1) * (n >= m ? 1 : -1);
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return Array.from({
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length: Math.floor((n - m) / d) + 1
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}, (_, i) => m + (i * d));
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};
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return sierpinski(order);
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})(4);
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