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 GeoAstro Applets |
 Astronomy |
 Chaos Game |
 Java |
 Miscel- laneous |
Entropy Applet
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Rules of this entropy game:
At start all cells are filled with the same color
(green).A random cell is selected: if green: green is replaced by red, if red: red is replaced by green.Continue. When equipartition (32 green cells, 32 red cells) is reached for the first time, the further distribution is evaluated graphically and numerically. |
The number N
of microstates (n cells, n1 red, n2
green, n= n1+n2)
is given by
Example N(2,2): n=4, n1=2, n2=2:
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N(64,0) = 1
N(63,1) = 64
N(62,2) = 2101
N(61,3) = 42,836
N(60,4) = 648,780
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N(33,31) = 1,784,054,207,724,775,680 ≈ 1.78 E18
N(33,31) = 1,839,796,536,686,813,696 ≈ 1.84 E18
Computing the entropy S by the formula S = ln N we get:
S(64,0) = 0
S(63,1) ≈ 4.159
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S(33,31) ≈ 42.025
S(32,32) ≈ 42.056
Equipartion (32,32) is achieved after 84.3 steps on average (standard deviation +/- 31.6):
Equipartion (18,18) is achieved after 43.7 steps on average (standard deviation +/- 18.7):
Testing the random number generator a standard deviation of 0.01 % is found:
| Books |
| Küppers, Bernd-Olaf: Die Berechenbarkeit
der Welt, Grenzfragen der exakten Wissenschaften. S.
Hirzel, Stuttgart 2012. Entropie und Zeitstruktur, S. 200-210 Eigen, Manfred, and Winkler, Ruth: Das Spiel, Naturgesetze steuern den Zufall. Pieper, München 1975. Kapitel 4:Statistische Kugelspiele |
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Updated: 2023 Oct 04
