-- =

------- = --zeroth row

------- = -- 1st row

------- = -- 2nd row

------- = --> TOTAL SUM

------- = -- 4th row

------- = -- 5th row

------- = -- 6th row

------- = -- 7th row

Game Model proposed by Paul & Tatiana Ehrenfest (1907)

Billions of years ago on Earth, How ordered structure emerged from the original chaos ? The problem of creation of information (order) and its selection and maintenance are possible in an open autocatalytic(template) system that is far from equilibrium. The accidental self-organization of chaos and the development of irreversible evolution are difficult to visualize. But we shall illustrate the emergence of order from chaos by resorting to game models. The above named model is illustrated below--

* We have a chessboard on which black & white draughtsmen are arranged arbitrarily occupying all the squares. We have 2 octahedral dice which are marked the number of horizontal rows as 1,2,.....,8 and on the other are the letters indicating the vertical columns a,b,.....,h.

* The Rules of the Game are : having thrown both dice, we replace a draughtsman, whose co-ordinates have been obtained on casting, by one of the other color. The outcome of the game is independent of the initial distribution : nearly equal number of white and black pieces will obtain on the board after a sufficient number of throws. The probability distribution will be Gaussian with a maximum at N/2 where N=64.

* Here a limitation of the fluctuation is clearly manifested. If there is a deviation from the equilibrium distribution,  the probability that this deviation will decrease increases in proportion to the deviation. The system is self regulating in the sense that it returns to the stable equilibrium. This is the general law of the behaviour of the system near the equilibrium.

EXPT: In the above simulation, white draughtman is replaced by 0 and black one by 1. The 2 dices are replaced by one grey,other light bluish text fields each having sides 0,1,2,3,4,5,6,7-- i.e eight faces from zero to 7. If on clicking the figure is 12, it means the draughtman of 1st  row and 2nd column shall be replaced. if it is 07, the draughtman of zeroth row and 7th column will be replaced. if it is 10, the draughtman of 1st row and zeroeth column will be replaced.