spiralSDF: Logarithmic Spiral Pattern Generator

Mathematical Spiral Construction in 2D Space

The spiralSDF function creates intricate spiral patterns by combining logarithmic radius transformation with angular positioning. This function generates distance fields that follow logarithmic spiral mathematics, producing visually appealing rotational patterns.

Mathematical Foundation

The spiral function operates through polar coordinate transformation:

$$d_{\text{spiral}} = |\sin(\text{fract}(\log(r) \cdot t + \theta \cdot k))|$$

where:

• $r = ||\mathbf{st} - \mathbf{center}||^2$ represents the squared distance from center
• $\theta = \arctan(y, x)$ provides angular position
• $t$ controls spiral tightness and frequency
• $k = 0.159 \approx \frac{1}{2\pi}$ normalizes angular scaling

The logarithmic transformation creates exponentially expanding spiral arms, while the fractional component generates periodic repetition.

Function Signature

Parameter	Type	Description
st	vec2	2D coordinate position
t	float	Spiral frequency and tightness control

Implementation Demonstrations

ライブエディター

const fragment = () => {
      const coord = uv.mul(2).sub(1)
      const time = iTime.mul(0.1)
      const spiral1 = spiralSDF(coord.mul(0.5).add(0.5), time.add(2))
      const spiral2 = spiralSDF(coord.mul(0.7).add(0.5), time.mul(1.3).add(4))
      const pattern = spiral1.mul(spiral2)
      const color = pattern.pow(0.5).mul(vec3(1, 0.7, 0.4))
      return vec4(color, 1)
}