Browse Items (42 total)

This is a visualization of the Lyapunov exponent δ for the r-sequence AABABAB AABABAB combined with a visualization of the Belousov-Zhabotinskii cone.

This image portrays the chaotic attractor according to a formula by I. Gumowski and C. Mira, which consists of quotients of polynomials. The variation of parameters leads to a manifold of patterns like the “three-winged” in this image. The repeated…

This image depicts the chaotic attractor according to a formula by I. Gumowski and C. Mira, which consists of quotients of polynomials. The variation of parameters leads to a manifold of patterns like the “seven-winged-bird” in this image. The…

The coordinates of this image are given by the concentrations of chemical substances. This image shows the transition to a periodic attractor. The points calculated first are colored blue, those computed last are yellow.

The coordinates of this image are given by the concentrations of chemical substances. This image shows the transition to a chaotic attractor (“ocean” in the lower part). Here, points are traced which initially lie within a rectangle. The content of…

This image depicts complex temporal phenomena called the logistic equation xn+1 = r xn (1-xn). In spite of its simple form, this equation shows a great variety in its dynamic behavior. For r < 3.57, the xn-series are periodic. For r ≥ 3.57,…

This image depicts the so-called logistic equation xn+1 = r xn(1-xn). In spite of its simple form, this equation shows a great variety in its dynamic behavior. For r < 3.57, the xn-series are periodic. For r ≥ 3.57, however, the series are…

This image shows the environment of the window with period 3 of the r-sequence AABAB AABAB ... The window is the same as in image M5, but here a different r-sequence was chosen. A small change in the sequence — in this case the repetition of A after…

This image depicts A-B-plane for the r-sequence AAABB AAABB ... To emphasize certain values of the Lyapunov exponent λ, lines of equal λ’s are drawn in white; in between, the color changes from black to goldgreen and back to black as λ increases.…

This image depicts the Lyapunov exponent for the r-sequence AAAAAABBBBBB AAAAAABBBBBB ... In those areas where two or more branches overlap two (or more) attractors coexist. (Note such areas in the other images of&lambda;, too). The coexistence of…