Semi-Chaotic Function Explorer

Compare the original index n with the composite growth substitution N = n^(n+1). The graph shows how the substitution slows phase growth and damps the sharper irregular behavior.

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

Composite: y_N(x) = x·sin(x^(1/N)) / ( x^(1/N)·sin(x^(1/(N+1))) + ε ), N = n^(n+1)

x max

Vertical clip

Blend to difference mode

Audio mode original

Audio speed

Drive

Volume

N = n^(n+1)

Reading

Original roughness

Composite roughness

Current audio y

Audio interpretation

Cyan = original n. Orange = substituted N = n^(n+1). Pale red = difference field. Roughness is estimated from average absolute step-change across the plotted curve. The audio generator can play the original field, the composite field, or their difference.