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Chaos: Generating Complexity from Simplicity
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
The most commonly used mapping to illustrate the phenomenon of chaos is the map x → 2x mod(1). This map is known as the 'unilateral shift' because, in the binary number system this map shifts all digits to the left by one decimal place, and truncates the integer. The second most commonly used paradigm of chaos is the Smale horseshoe whose complexity is essentially the bilateral shift obtained when we simply shift without truncation in some symbol system. Neither of these paradigms fullydoi:10.1142/s021812749700162x fatcat:v56j2bduz5bunejhwkhswnvgym