Samuel D Sazo Sazo

A Closed-Boundary Convergence Theorem for the Golden-Ratio Contraction Map(LLM)

Abstract We examine the affine contraction[ T(x)=\varphi+\varphi^{-7}(x-\varphi) ]on the real line, where (\varphi=(1+\sqrt{5})/2) is the golden ratio. The map is a linear contraction with unique fixed point (\varphi) and ratio (r=\varphi^{-7}\approx0.03444). The orbit satisfies...

A Closed-Boundary Convergence Theorem for the Golden-Ratio Contraction Map(LLM)

Abstract We examine the affine contraction[ T(x)=\varphi+\varphi^{-7}(x-\varphi) ]on the real line, where (\varphi=(1+\sqrt{5})/2) is the golden ratio. The map is a linear contraction with unique fixed point (\varphi) and ratio (r=\varphi^{-7}\approx0.03444). The orbit satisfies...