The SOC in cells’ living expectations of Conway’s Game of Life and its extended version

In self-organized systems such as Conway’s Game of Life (CGL). Wikipedia, Conway’s game of the life, https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life., though whether the single cell will survive or die seems unpredictable, the log–log distribution of all cells living frequency satisfies the 1/f linear law, thus meets the Self-organized Criticality(SOC) rule, which not only proves that CGL is a self-organized system, but more significantly, that the chance of living for each cell is spatial heterogeneous, and is statistical fractal.After carried out CGL, the specified iterative period which begins with a random initial condition and ends when it reaches the homeostasis, add up all the states which the living cells are marked by 1s, and the dead are marked by 0s. The resulted sum picture consisting of cells having its gray level representing the living times during the iterative process. By plotting the gray level distribution of the sum picture on log–log scale, the graph indicates the spatial living expectations distributions. Then we find the curve of the graph satisfies the Self-organized Criticality(SOC) rule, showing its linear feature in the intermediate zone, which also has name of 1/f feature.To examine its universality, we designed a more complicated self-organized cellular automata with each cell having five possible states thus the rule table becomes more complicated. As expected, the consequence shows the similar feature, and the linear feature is even more obvious when the similar experiments are carried out.To conclude, it is a new discovery of SOC from a new perspective. And with the self-organized systems expanding to other different rule tables, this feature may still be satisfied.More further, considering the natural self-organized systems of living creatures, the spatial living expectations of different phenotypes may satisfy the 1/f law, too. Though we regard this as an inspirational orientation, the supposition needs more designed experiments to prove.