RandomSpirograph-FrankZ

art/RandomSpirograph-FrankZ/index.js

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+/*
+@title: Random Spirograph
+@author: FrankZ
+@snapshot: snapshot1.png
+*/
+
+// actually important values
+let RANDOM = true;
+let wheelRadius = 28; // somewhat breaks if greater than the outer circle's
+let holeLocation = 12; // hole distance from edge of wheel, should be less than wheelRadius
+
+
+
+let resolution = 2; // degrees between each point, lower = smoother curve
+
+const drawCircle = true;
+const drawWheel = false;
+
+// 60 is good, has a lot of factors and is big
+let outerRadius = 60;
+
+// randomize important values with reasonable ranges
+if (RANDOM) {
+  wheelRadius = bt.randIntInRange(2, outerRadius - 2);
+  holeLocation = bt.randIntInRange(0, wheelRadius - 1);
+};
+
+const width = 125;
+const height = 125;
+setDocDimensions(width, height);
+
+drawLines(bt.text("Wheel: " + wheelRadius.toString(),[1,8],1.2));
+drawLines(bt.text("Hole: " + holeLocation.toString(),[1,1],1.2));
+
+// outer circle turtle if drawCircle is true
+const circle = new bt.Turtle();
+  circle.setAngle(180);
+  circle.jump([62.5, 62.5 + outerRadius]);
+  circle.arc(360, outerRadius);
+if (drawCircle) {
+  drawLines(circle.lines());
+};
+// wheel turtle if drawWheel is true
+const wheel = new bt.Turtle();
+  wheel.setAngle(180);
+  wheel.jump([62.5, 62.5 + outerRadius]);
+  wheel.arc(360, wheelRadius);
+  wheel.jump([62.5, 63.5 + outerRadius - holeLocation]);
+  wheel.arc(360, 1);
+if (drawWheel) {
+  drawLines(wheel.lines());
+};
+
+// recursive calculation to find the greatest common factor
+function gcd(a, b) {
+  if (b === 0) {
+    return a;
+  };
+  return gcd(b, a % b);
+};
+
+// unnecessarily long calculation to find revolutions needed to loop spirograph
+let revolutions = ((outerRadius * wheelRadius) / (gcd(outerRadius, wheelRadius))) / (outerRadius);
+
+const spirograph = new bt.Turtle();
+ spirograph.jump([62.5, 62.5 + outerRadius - holeLocation]);
+
+// "simulates" the wheel rotating while moving along the path of the center of the wheel
+for (let time = 0; time <= revolutions*360; time += resolution) {
+  let timeRadians = time * (Math.PI/180);
+  let wheelCenterPointX = (outerRadius - wheelRadius) * Math.sin(timeRadians) + 62.5;
+  let wheelCenterPointY = (outerRadius - wheelRadius) * Math.cos(timeRadians) + 62.5;
+  let pointX = wheelCenterPointX - (wheelRadius - holeLocation) * Math.sin(timeRadians * (outerRadius / wheelRadius - 1));
+  let pointY = wheelCenterPointY + (wheelRadius - holeLocation) * Math.cos(timeRadians * (outerRadius / wheelRadius - 1));
+  spirograph.goTo([pointX, pointY]);
+};
+
+drawLines(spirograph.lines());
+