Another update from ingydotnet^djgoku

Task/Sierpinski-triangle/JavaScript/sierpinski-triangle-1.js

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+// A Sierpinski triangle of order N,
+// constructed as Pascal's triangle mod 2
+// and mapped to 2^N lines of centred {1:asterisk, 0:space} strings
+
+(function (n) {
+  var nRows = Math.pow(2, n),
+      lstSierpinski = sierpinski(nRows).map(asciiBinary),
+
+      nBaseWidth = lstSierpinski[nRows - 1].length;
+
+  return lstSierpinski.map(
+    function (s) {
+      return centreAligned(s, nBaseWidth);
+    }
+  ).join('\n');
+})(4);
+
+// A Sierpinski sieve of n rows
+// (Pascal triangle mod 2)
+// n --> [bool]
+function sierpinski(n) {
+  return pascalTriangle(n).map(
+    function (line) {
+      return line.map(function (x) {
+        return x % 2;
+      });
+    }
+  )
+}
+
+// A Pascal triangle of n rows
+// n --> [[n]]
+function pascalTriangle(n) {
+
+  // Sums of each consecutive pair of numbers
+  // [n] --> [n]
+  function pairSums(lst) {
+    return lst.reduce(function (acc, n, i, l) {
+      var iPrev = i ? i - 1 : 0;
+      return i ? acc.concat(l[iPrev] + l[i]) : acc
+    }, []);
+  }
+
+  // Next line in a Pascal triangle series
+  // [n] --> [n]
+  function nextPascal(lst) {
+    return lst.length ? [1].concat(
+      pairSums(lst)
+    ).concat(1) : [1];
+  }
+
+  // Each row is a function of the preceding row
+  return n ? Array.apply(null, Array(n - 1)).reduce(
+    function (a, _, i) {
+      return a.concat(
+        [nextPascal(a[i])]
+      );
+    }, [
+      [1]
+    ]
+  ) : [];
+}
+
+// [bool] --> s
+function asciiBinary(lst) {
+  return lst.map(
+    function (x) {
+      return x ? '*' : ' ';
+    }
+  ).join(' ');
+}
+
+// Space-padded to left and right
+// s --> n --> s
+function centreAligned(s, n) {
+  var lngWhite = n - s.length,
+    lngMargin = lngWhite > 0 ? Math.ceil(lngWhite / 2) : 0,
+    strMargin = lngMargin ? Array(lngMargin + 1).join(' ') : '';
+
+  return strMargin ? strMargin + s + strMargin : s;
+}