Inner angle of triangle on unit circle made of consecutive three points generated by chaotic map

Abstract

Inner angle of triangle made of consecutive three points on unit circle is investigated. We use two methods to plot points. One is plotting random numbers whose distribution is uniform. Another is plotting consecutive numbers obtained by a map which generates complex chaotic sequences with constant power. We focus on an inner angle at the middle point in consecutive three points. An angle for chaotic sequence is found to be different from one for uniform random sequence.

Correlational properties of two-dimensional solvable chaos on the unit circle

“…Knowledge on solvable chaos is useful for designing random number generators [1,2,3,4] and Monte Carlo integration [5]. The idea of applying chaos theory to randomness has produced important works recently [6,7,8,9].…”