Scale Transformation Function

The Scale Transformation Function is the dimensionless factor Ψ△(k) in the Golden Ratio Recursion Law that modifies golden-ratio scaling when a recursive state is carried up k scale levels. In that law a recursive state at level n + k equals the state at level n multiplied by φᵏ, the golden ratio raised to the scale increment, and by Ψ△(k). The golden-ratio factor gives the proportional growth; Ψ△(k) is the level-dependent adjustment the book includes alongside it. The law as a whole expresses the fractal symmetry the book attributes to the UniSphere, in which the same recursive pattern holds from a Prime Pulse Bifurcation to the structure of galaxies. The book lists Ψ△(k) as dimensionless [∅]. It connects to Golden Ratio Recursion Law, Self-Similar Structure, Scale Transition Law, Scale Emergence and Prime Pulse Bifurcation.