Revelations of the Yin–Yang Law in the Cellular Automata of the Game of Life

These past couple of days I have been trying to play with the Game of Life. The game itself is very simple—just iteration of some simple rules—but under certain parameter conditions it can produce complex emergence, which is a truly remarkable point.

Generally speaking, mechanical calculations often yield mechanical results, but under specially constructed parameters subtle phenomena can arise and complex behavioral rules can emerge. Its greatest significance lies in the fact that these complex and hard-to-predict rules are produced by iterating extremely simple rules.

This illustrates a philosophical point: not all complex phenomena arise from complex causes, but neither do all simple rules necessarily iterate into complex results—only when things fall subtly and precisely under certain conditions can such effects be produced.

And these results that emerge are often hard to foresee intuitively. Take opposing things: when one side’s strength becomes great enough to produce an imbalance, the other side is destroyed—this is common sense. But under certain conditions, even when strength and weakness differ by a huge margin, they can together constitute a system and coexist.

The key to this is forming a dissipative system. The key points of a dissipative system are: (1) the system must be open—it is a dissipative structure system; (2) it must be far from equilibrium in order to enter the nonlinear region; (3) there must be nonlinear interactions among the various parts of the system; (4) some parameters of the system experience fluctuations, and when fluctuations change beyond a certain threshold the steady state becomes unstable and the system undergoes a mutation, so that some highly ordered state may emerge.

Under such conditions, self-organization phenomena will arise; the complexity of the natural world is very likely caused by this—life, for example.

The conditional rules of cellular automata are as follows: if two living cells surround a cell, it remains in its original state; if three living cells surround it, it survives; in all other cases the cell is considered unable to survive—either there are no surrounding cells or too many cells occupying too many resources.

The key here lies in the parameters. Whether two cells determine that state is maintained, or three cells enable survival, remove either condition and the cellular automaton can hardly continue computing.

This is one state from a random cellular automaton computation. As computation continues, some patterns maintain their original shapes while moving continuously, or undergo deformation; some new patterns keep emerging, while some old cells die and wither. As long as computation continues, it will keep iterating and never end.

 If only one surrounding cell survives, then whether the central cell survives or dies, under this rule the automaton will keep computing—but mainly points and lines appear, without more complex patterns. As long as this parameter value is no greater than three, the automaton can continue computing on its own, producing patterns similar to various kinds of noise. When it is greater than three, a rapid “clearing” phenomenon occurs, leaving only a few cells at the margins able to survive.

And if one or two are allowed for the middle cell to survive, the result is rapid convergence into patterns of dots and horizontal lines.

When slightly more complex rules are added—if two living neighbors make the middle live, and one living neighbor makes the middle retain its original state—it will also rapidly converge into a state similar to the above, though a few active points will appear.

If one uses three cells to decide life and two cells to maintain state as larger parameters—for example, four cells deciding to maintain the original state—one can also obtain fairly interesting results; the patterns seem to use the surroundings as a boundary and continuously erupt something toward the middle.

If this parameter is further modified to five, under certain conditions patterns will appear that rise continuously from the bottom, like bubbles. What is interesting is that this pattern seems always to bubble from bottom to top.

When it is 6 or greater, everything seems suppressed at the surroundings with no special changes.

The middle point of a cellular automaton and the eight surrounding points form exactly nine points, which matches the form of the Nine Palaces. What would happen if we applied the Five Phases generation-and-conquest rules of the Nine Palaces inside?

Here the rules use the Five Phases of the central palace to influence the surrounding eight palaces. What is interesting is that it can still keep computing like a cellular automaton, and one can see that through Five Phases generation and conquest, all the lines here show regularity, and this angle happens to fall between Chensi and Xuhai—the exact angle of the Heaven Gate and Earth Door. That is to say, the Nine Palaces use the directional logic of Five Phases generation and conquest to simulate the force direction of the Heaven Gate and Earth Door, and this force is manifested through the flow of yin and yang. This shows that all things, as long as they keep iterating according to the laws of the Nine Palaces, can keep computing without end.

But this regularity is very indistinct, so I considered: what if instead of the Nine-Palace Five Phases, I used the Hetu Five Phases? When Hetu Five Phases were adopted, astonishing results were obtained—no matter what the initial state, after computation with Hetu Five Phases, an ordered pattern would eventually form:

Very strange changes occurred: a clear boundary between yin and yang appeared. The left side formed vertical stripes, while the right side became a noise-like pattern. If this were a circle, it would call to mind the taiji diagram. This illustrates a point: using Hetu Five Phases can make objective information become ordered. This offers a revelation: regularizing the objective world with Hetu Five Phases divides it into regularized and non-regularized sides; as yin and yang, the Hetu Five Phases side shows the characteristic of evenly divided yin and yang. Because large numbers of random numbers are used in the middle to arbitrarily influence different regions, this suggests a possibility—that of predicting and grasping the likelihood of things—because no matter how many random numbers influence the process of change, everything will ultimately emerge unified under regularity.

However, the most important thing in grasping yin and yang is not how to construct chaos; quite the opposite, it is how to eliminate chaos—to construct certain conditions that remove the intervening random influences and ensure that the ultimate result can be obtained directly from the initial state. This is treated in a separate article.