Nested Resonance Map

This maps the formula as a field rather than a single oscillator value, so you can see where it stays smooth, where it bends, and where it begins to spike.

y = x·sin(x^(1/n)) / ( x^(1/n)·sin(x^(1/(n+1))) + ε )

x max

n min

n max

slice n

color mode

clip

Pattern reading

The map compares one oscillatory scale against a deeper root scale. Warm ridges mark strong positive amplification, cool troughs mark phase opposition, and pale boundaries show where the denominator approaches zero and the system becomes sensitive.

As n rises, the roots flatten the phase growth, so the field usually becomes broader and more slowly varying. Smaller ε reveals sharper structures; larger ε smooths them.

min –

max –

mean –

sensitive pixels –

negative

positive

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

Slice plot across x for the selected n.