Pulse Core Lexicon

Recursive Complexity Growth

Definition

Recursive Complexity Growth is the nonlinear accumulation of computational complexity, following P(n) = (n+1)², that BPT puts in place of the linear progression of classical harmonics and that produces Nonlinear Harmonic Spectra. In classical systems the nth harmonic of a fundamental f_0 is f_n = n × f_0, a linear additive series. BPT replaces this with Recursive Complexity Growth, reflecting the computational architecture of the binary substrate: harmonics emerge from Prime Pulse Bifurcation working through Recursive State Evolution, where each generation inherits and amplifies the computational load of those before. The load grows as L(n) = L_0 + n(n+1)/2, and that quadratic growth is what shows up in the frequency domain as harmonics scaling with (n+1)², linking computational load to pulse density and Temporal Drag. The current definition states the growth pattern as P(n) = (n+1)², where P(n) is the pulse density and n the recursion depth. It connects to Nonlinear Harmonic Spectra, Harmonic Complexity Scaling, Computational Load Accumulation, Recursive State Evolution, Prime Pulse Bifurcation and the Harmonic Origin Pulse.

Mathematical Expression

From the book · Chapter 7 · Harmonic Complexity and the Recursive Spectrum

P(n) = (n + 1)² [∅]

Where:

  • L(n) [∅] - simplified cumulative computational load
  • P(n) [∅] - pulse density function
  • n [∅] - recursion depth index
  • [∅] - quantities without physical units, pure numerical ratios or mathematical constants

Technical Details

Category Concept

Chapter Chapter 7

Importance

Related Terms