The Ibaguner–Euler Constant and Fractal Scaling in IFO Cascades

We introduce the constant 1/e as a natural scaling parameter arising in cascades generated by the Ibaguner Fractal Operator (IFO). The interaction between exponential amplification and hyperbolic tangent saturation leads to a bounded multiplicative process whose contraction factor approaches 1/e. We refer to this quantity as theIbaguner–Euler constant. We show that this constant naturally determines the scaling law of the cascade and yields a simple logarithmic formula for the associated fractal dimension. Connections to distance-set problems and fractal measures are also discussed.