Home

Site Map

Search

physics,
                      astronomy, simulation, entropy, cellular
                      automaton, Java applet
GeoAstro
Applets

Astronomy
physics,
                    astronomy, simulation, entropy, cellular automaton,
                    Java applet
Chaos Game
physics,
                      astronomy, simulation, entropy, cellular
                      automaton, Java applet
Java
physics,
                    astronomy, simulation, entropy, cellular automaton,
                    Java applet
Miscel-

laneous

Entropy Applet



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

formula microstates

Example N(2,2): n=4, n1=2, n2=2:


























number of microstates

N(64,0) = 1
N(63,1) = 64
N(62,2) = 2101
N(61,3) = 42,836
N(60,4) = 648,780
.
.
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
.
S(33,31) ≈ 42.025
S(32,32) ≈ 42.056

entropy

Equipartion (32,32) is achieved after 84.3 steps on average (standard deviation +/- 31.6):

steps for equipartition

Equipartion (18,18) is achieved after 43.7 steps on average (standard deviation +/- 18.7):

equipartition

Testing the random number generator a standard deviation of 0.01 % is found:

random

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
Web Links

Updated: 2023 Oct 04