Inverse: Mathematical Reciprocal Transform

Reciprocal Field Generator for Dynamic Visual Mathematics

The inverse function computes the mathematical reciprocal transformation f(x) = 1/x, creating infinite field gradients and hyperbolic distributions. This function transforms linear space into non-linear domains where proximity to zero creates dramatic amplification effects.

Mathematical Foundation

Property	Definition	Mathematical Expression
Basic Transform	Reciprocal operation	inverse(x) = 1/x
Domain	All real numbers except zero	x ≠ 0
Range	All real numbers except zero	y ≠ 0
Asymptotic Behavior	Vertical at zero, horizontal at infinity	Approaches infinity at zero, approaches zero at infinity
Symmetry	Hyperbolic reflection	f(-x) = -f(x)

Hyperbolic Wave Distortion

This demonstration uses reciprocal transformation to create hyperbolic wave fields where oscillating patterns near zero generate infinite gradients and spectacular visual dynamics.

ライブエディター

const fragment = () => {
      const time = iTime.mul(2)
      const pos = uv.sub(0.5).mul(6)

      const wave = pos.x.add(time.sin().mul(0.8)).sin().mul(0.3).add(0.5)
      const hyperField = inverse(wave.add(0.1))

      const distortion = pos.y.add(hyperField.mul(0.2))
      const pattern = distortion.sin().mul(0.5).add(0.5)

      const r = pattern.pow(3)
      const g = hyperField.abs().mul(0.1).mod(1)
      const b = time.cos().mul(0.5).add(0.5)

      return vec4(r, g, b, 1)

}