mmin: Multi-Value Minimum Function

Component-wise Minimum Extraction

The mmin function finds the smallest value among multiple inputs or vector components. It's a utility function that works with 2-4 individual values or extracts the minimum component from vec2, vec3, or vec4 vectors.

Mathematical Definition:

$\text{mmin}(\mathbf{v}) = \min\{v_1, v_2, v_3, v_4\}$

For quantum state analysis in 4-dimensional space:

$\mathbf{v} \in \mathbb{C}^4 \Rightarrow \text{mmin}(\mathbf{v}) = v_i \text{ where } i = \arg\min_j |v_j|$

The convergence theorem establishes stability bounds:

$\forall \mathbf{v} \in \mathbb{R}^n: \text{mmin}(\mathbf{v}) \leq v_i \quad \forall i \in \{1,2,\ldots,n\}$

Harmonic attractor principle:

$\lim_{t \to \infty} \text{mmin}(\mathbf{v}(t)) = \text{stable equilibrium point}$

This function is useful for finding the smallest component in color values, determining threshold values in multi-channel data, or creating effects based on the weakest influence among multiple factors.

ライブエディター

const fragment = () => {
      const t = iTime.mul(0.3)
      const p = uv.sub(0.5)

      const h1 = p.x.mul(2.8).add(t.mul(0.9))
      const h2 = p.length().mul(3.5).add(t.mul(1.1))
      const h3 = p.x.mul(p.y).mul(1.7).add(t.mul(1.8))
      const h4 = p.x.add(p.y).mul(4.2).add(t.mul(0.7))

      const oscillators = vec4(h1.cos().mul(h1.sin()),
                              h2.mul(5).sin().mul(0.8),
                              h3.mul(3).cos(),
                              h4.mul(1.9).sin().mul(1.2))

      const convergence = mmin(oscillators)
      const field = p.length().mul(6).sub(convergence.mul(8)).cos().mul(convergence.abs())

      return vec4(field.mul(vec3(0.3, 0.7, 1)), 1)

}