pow7: Seventh Power Function

Extreme Non-Linear Amplification

The pow7 function raises input values to the seventh power ($x^7$). This creates very strong non-linear amplification - values near zero become extremely small, while values above 1 become extremely large. Like other odd powers, pow7 preserves the sign of negative inputs.

$$\text{pow7}(x) = x^7 = x^2 \cdot x^2 \cdot x^2 \cdot x$$

The septenary function demonstrates critical mathematical transcendence: ultra-steep acceleration with derivative $7x^6$, extreme compression for $|x| < 1$ approaching zero faster than any lower power, and preservation of directional orientation through odd-power symmetry. The transformation creates natural heptagonal resonance patterns due to its fundamental relationship with seven-fold geometry.

High-Contrast Visual Effects

The extreme non-linearity of pow7 creates sharp contrast effects where small input variations produce dramatically different outputs, useful for creating high-contrast patterns and dramatic visual transitions.

ライブエディター

const fragment = () => {
      const center = uv.sub(0.5)
      const radius = center.length()
      const angle = center.y.atan2(center.x)

      const heptaPhase = angle.mul(3.5).add(iTime.mul(0.5))
      const radialPulse = radius.mul(7).sub(iTime.mul(2))

      const septenaryCore = pow7(heptaPhase.sin().mul(0.4))
      const radialTransform = pow7(radialPulse.sin().mul(0.35))

      const mysticalResonance = septenaryCore.add(radialTransform.mul(0.7))
      const crystallineIntensity = mysticalResonance.abs().pow(0.2)

      const heptaSymmetry = angle.mul(7).cos().mul(0.5).add(0.5)

      const r = crystallineIntensity.mul(heptaSymmetry)
      const g = crystallineIntensity.mul(septenaryCore.abs().add(0.3))
      const b = crystallineIntensity.mul(radialTransform.abs().mul(0.8).add(0.2))

      return vec4(r, g, b, 1)

}