kaleidoscope: Angular Symmetry Transformation

Radial Mirror Reflection System

The kaleidoscope functions create angular symmetry by dividing coordinate space into segments and mirroring content across radial boundaries. This produces kaleidoscopic effects with configurable segment counts and rotation phases.

Mathematical Foundation

The transformation operates in polar coordinates:

$$\theta' = \min(\theta \bmod \alpha, \alpha - (\theta \bmod \alpha))$$

Where $\alpha = \frac{2\pi}{n}$ is the segment angle for $n$ segments, ensuring each segment contains a mirrored copy of the original pattern.

Function Variants

Function	Parameters	Default Values
kaleidoscope	coord, segmentCount, phase	-
kaleidoscopeDefault	coord	8 segments, 0° phase
kaleidoscopeCount	coord, segmentCount	0° phase

Live Editor

const fragment = () => {
      const kaleido = kaleidoscopeCount(uv, 6)
      const pattern = sin(kaleido.x.mul(20)).mul(sin(kaleido.y.mul(20)))
      const color = pattern.mul(0.5).add(0.5)
      return vec4(vec3(color), 1)
}

Result

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