Data update

Task/Babylonian-spiral/JavaScript/babylonian-spiral.js

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+function babylonianSpiral(stepCount) {
+    const tau = 2 * Math.PI;
+    const squares = Array(stepCount + 1).fill(0).map((_, i) => i * i);
+    const points = [[0, 0], [0, 1]];
+    let norm = 1;
+
+    for (let step = 0; step < stepCount - 2; ++step) {
+        const previousPoint = points[points.length - 1];
+        const theta = Math.atan2(previousPoint[1], previousPoint[0]);
+        let candidates = [];
+
+        while (candidates.length === 0) {
+            norm += 1;
+            for (let i = 0; i < stepCount; ++i) {
+                const a = squares[i];
+                if (a > norm / 2) break;
+                for (let j = Math.floor(Math.sqrt(norm)) + 1; j >= 0; --j) {
+                    const b = squares[j];
+                    if (a + b < norm) break;
+                    if (a + b === norm) {
+                        const nextPoints = [
+                            [i, j], [-i, j], [i, -j], [-i, -j],
+                            [j, i], [-j, i], [j, -i], [-j, -i]
+                        ];
+                        candidates.push(...nextPoints);
+                    }
+                }
+            }
+        }
+
+        let minimum = null;
+        let minimumValue = tau;
+        for (const candidate of candidates) {
+            const value = (theta - Math.atan2(candidate[1], candidate[0]) + tau) % tau;
+            if (value < minimumValue) {
+                minimumValue = value;
+                minimum = candidate;
+            }
+        }
+        points.push(minimum);
+    }
+
+    // Accumulate points
+    for (let i = 0; i < points.length - 1; ++i) {
+        points[i + 1] = [
+            points[i][0] + points[i + 1][0],
+            points[i][1] + points[i + 1][1]
+        ];
+    }
+
+    return points;
+}
+
+function main() {
+    const points = babylonianSpiral(40);
+    console.log("The first 40 points of the Babylonian spiral are:");
+    for (let i = 0, column = 0; i < 40; ++i) {
+        const pointStr = `(${points[i][0]}, ${points[i][1]})`;
+        process.stdout.write(pointStr.padStart(10));
+        if (++column % 10 === 0) {
+            console.log();
+        }
+    }
+}
+
+main();