Generalized Resonance Map

This version separates the three root-scales into independent variables, so you can see how numerator phase, denominator scale, and denominator phase negotiate the field.

y = x·sin(x^(1/n₁)) / ( x^(1/n₂)·sin(x^(1/n₃)) + ε )

x max

vary on vertical axis

color mode

n₁ fixed / min

n₁ max (only if varying)

n₂ fixed / min

n₂ max (only if varying)

n₃ fixed / min

n₃ max (only if varying)

slice value (for varying axis)

clip

The map reveals how three independent resonance roles interact. White contours mark regions where the denominator becomes sensitive and amplification can sharpen abruptly.

Use “vary on vertical axis” to choose which n changes from bottom to top. The other two stay fixed.

min –

max –

mean –

sensitive pixels –

negative

positive

Horizontal axis: x. Vertical axis: selected varying n. White contours indicate denominator sensitivity.

Slice plot across x for the selected vertical-axis value.