Apollonian

an Apollonian gasket: every gap between three touching circles is filled by the one circle that touches all three, and the color changes with each generation, so the filling order shows (apollonianGasket)

Run

swift run --package-path Examples Example-Patterns-Apollonian

Source

Examples/Patterns/Apollonian/Sketch.swift

import Ollin

/// An Apollonian gasket: three circles kiss inside a rim, and every three-way
/// gap is filled by the one circle that exactly touches all three, forever
/// (here, down to a few pixels). The foam is a closed form with no randomness,
/// so it's built once; what moves is the color, sweeping through the
/// generations so the filling order becomes visible.
@main
final class ApollonianFoam: Sketch {
    override var loopDuration: Double? { 8 }

    private var foam: [Circle] = []

    override func setup() {
        foam = apollonianGasket(in: Circle(center: bounds.center, radius: width * 0.44),
                                minRadius: 2.5 * scale)
    }

    override func draw() {
        background(Color(hex: 0x0E1116))

        noFill()
        stroke(Color(hex: 0x2A3140))
        strokeWeight(2 * scale)
        drawCircle(center: bounds.center, radius: width * 0.44)

        let phase = loopProgress(over: 8)
        noStroke()
        for (i, circle) in foam.enumerated() {
            // Age runs with the generation order; the wave loops through it.
            let age = Double(i) / Double(foam.count)
            let wave = pingPong(over: 1, phase: phase - age)
            fill(Color.mix(Color(hex: 0x1D5C63), Color(hex: 0xF9DC5C), wave * wave * wave)
                .withAlpha(0.92))
            drawCircle(circle)
        }
    }
}