lorenz-omay

art/lorenz-omay/index.js

@@ -0,0 +1,95 @@
+/*
+@title: Lorenz Attractor
+@author: Leonard (Omay)
+@snapshot: lorenz.png
+
+The Lorenz System is a system of Ordinary Differential 
+Equation, and a popular example of a chaotic pattern. 
+This is a pattern that, while technically predictable, 
+slight differences in the initial state lead to 
+drastically different results. It is commonly associated 
+with the Butterfly Effect, which says that a flap of a 
+butterflys wings could lead to a disaster, due to a 
+slight change in conditions leading to significant 
+changes in outcome. The Lorenz Attractor also looks 
+like a butterfly when plotted on the XZ plane, which 
+is a nice coincidence.
+Wikipedia: https://en.wikipedia.org/wiki/Lorenz_system
+*/
+
+const rho = bt.randInRange(18, 38); // default 28
+const sigma = bt.randInRange(0, 20); // default 10
+const beta = bt.randInRange(2 / 3, 14 / 3); // default 8 / 3
+
+const xAxis = "xyz".split("")[bt.randIntInRange(0, 2)]; // Change to "x", "y", or "z"
+const yAxis = "xyz".split("").filter(v => v !== xAxis)[bt.randIntInRange(0, 1)]; // Change to "x", "y", or "z"
+
+const dt = 0.01;
+const finalIter = 10000;
+
+const width = 125;
+const height = 125;
+const margin = 10;
+
+setDocDimensions(width, height);
+
+let iter = 0;
+let lines = [];
+
+let x = 1;
+let y = 1;
+let z = 1;
+
+let minA = Infinity, maxA = -Infinity;
+let minB = Infinity, maxB = -Infinity;
+
+let prevA = 0, prevB = 0;
+
+while (iter < finalIter) {
+  let xt = x;
+  let yt = y;
+  let zt = z;
+  x = xt + sigma * (yt - xt) * dt;
+  y = yt + (xt * (rho - zt) - yt) * dt;
+  z = zt + (xt * yt - beta * zt) * dt;
+
+  let a = 0, b = 0;
+
+  if (xAxis === "x") a = x;
+  else if (xAxis === "y") a = y;
+  else if (xAxis === "z") a = z;
+
+  if (yAxis === "x") b = x;
+  else if (yAxis === "y") b = y;
+  else if (yAxis === "z") b = z;
+
+  if (a < minA) minA = a;
+  if (a > maxA) maxA = a;
+  if (b < minB) minB = b;
+  if (b > maxB) maxB = b;
+
+  if (iter > 0) {
+    lines.push([[prevA, prevB], [a, b]]);
+  }
+
+  prevA = a;
+  prevB = b;
+
+  iter++;
+}
+
+let scaleX = (width - 2 * margin) / (maxA - minA);
+let scaleY = (height - 2 * margin) / (maxB - minB);
+let scale = Math.min(scaleX, scaleY);
+
+let offsetX = margin + (width - 2 * margin - (maxA - minA) * scale) / 2;
+let offsetY = margin + (height - 2 * margin - (maxB - minB) * scale) / 2;
+
+lines = lines.map(val => {
+  return [
+    [(val[0][0] - minA) * scale + offsetX, (val[0][1] - minB) * scale + offsetY],
+    [(val[1][0] - minA) * scale + offsetX, (val[1][1] - minB) * scale + offsetY]
+  ];
+});
+
+drawLines(lines);