Browse Items (42 total)
- Collection: 1988 - Dyn. Pattern Form. in Chem. and Math.
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C1 - Chaos
This image depicts experimentally observed chaotic patterns, caused by interaction of chemical waves (Belousov-Zhabotinskii reaction) with convective flow, which is induced by evaporation.
C2 - Spiral waves
Spiral waves, which evolved from the state shown in image C1 by self-organization after evaporation had been prevented. Similar patterns can be observed in slime molds, the flickering heart muscle, and the retina (compare M15 and C5)
M0 - Composition of M14 and C8
This is a visualization of the Lyapunov exponent δ for the r-sequence AABABAB AABABAB combined with a visualization of the Belousov-Zhabotinskii cone.
M1 - 'Three-winged' pattern of a chaotic attractor.
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…
M2 - 'Seven-winged bird' pattern of a chaotic attractor
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…
M3 - Concentrations of chemical substances in the transition to a periodic attractor
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.
M4 - Concentrations of chemical substances in the transition to a chaotic attractor
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…
M5 - complex temporal phenomena is the so-called logistic equation xn+1 = r xn (1-xn).
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,…
M6 - complex temporal phenomena is the so-called logistic equation xn+1 = r xn(1-xn).
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…
M7 - Lyapunov exponent for the r-sequence AABAB AABAB ...
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…
