# Computer arithmetic, chaos and fractals

Julian I Palmore, Charles Herring

Research output: Contribution to journalArticle

### Abstract

In this paper we explore aspects of computer arithmetic from the viewpoint of dynamical systems. We demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. We show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.

Original language English (US) 99-110 12 Physica D: Nonlinear Phenomena 42 1-3 https://doi.org/10.1016/0167-2789(90)90069-2 Published - Jun 1990

### Fingerprint

chaos
fractals
dynamical systems
floating point arithmetic
cats
floating
integers
generators
shift

### ASJC Scopus subject areas

• Statistical and Nonlinear Physics
• Condensed Matter Physics

### Cite this

Computer arithmetic, chaos and fractals. / Palmore, Julian I; Herring, Charles.

In: Physica D: Nonlinear Phenomena, Vol. 42, No. 1-3, 06.1990, p. 99-110.

Research output: Contribution to journalArticle

Palmore, Julian I ; Herring, Charles. / Computer arithmetic, chaos and fractals. In: Physica D: Nonlinear Phenomena. 1990 ; Vol. 42, No. 1-3. pp. 99-110.
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