Fractal

Fractal: A complex geometric pattern exhibiting self-similarity in that small details of its structure viewed at any scale repeat elements of the overall pattern.

Fractal curves are generated from an initial curve (often a regular polygon) and one or more replacement curves. Repeatedly, each line is replaced by a properly scaled copy of one of the replacement curves.

Let's draw a Lévy C curve

Begin with drawing a simple line.


						function offsetPoint(start, angle, distance) {
							return p5.Vector
								.fromAngle(radians(angle), distance)
								.add(start);
						}
						function drawCurve(start, angle, distance) {
							var endPt = offsetPoint(start, angle, distance);
							line(start.x, start.y, endPt.x, endPt.y);
						}

Replace the line with the right angle pattern.

				
						var d2 = d1 * someScale; // <-- what's this number?
						var midPt = offsetPoint(start, angle + 45, d2);
						var endPt = offsetPoint(midPt, angle - 45, d2);
						line(start.x, start.y, midPt.x, midPt.y);
						line(midPt.x, midPt.y, endPt.x, endPt.y);

				
						someScale = 0.7071069;

Recursive: Relating to or involving the repeated application of a rule, definition, or procedure to successive results.

				
						function someFn(param) {
							//...
							someFn(newParam);
							//...
						}

				
						function drawCurve(start, angle, d1, replacements) {
							if (replacements == 0) {
								// draw the line
							} else {
								// call draw curve for each line in
								// the pattern.
								drawCurve(..., replacements - 1);
							}
						}

Let's look at some other curves.