Network Analysis of Baker's Map Implemented in a Fixed-Point Arithmetic Domain

In the past five decades, the dynamics of Baker's map in an infinite precision world have been extensively explored. However, the real structure of Baker's map when implemented in a fixed-point arithmetic domain remains unknown. This paper gives an explicit formulation for the quantized Baker's map. We then demonstrate that the maximum in-degree of the functional graph of Baker's map is invariant under any level of fixed-point arithmetic precision. Intriguingly, we observe a self-similarity phenomenon in the functional graph of a specific Baker's map with incremental increases in precision. These findings demonstrate the consistency of Baker's map across varying precision levels. This can be utilized to streamline the dynamic analysis and application design of Baker's map and its variants in finite precision environments.