Irregularity and Movement

Life is a stream

Life is manifested by irregularity  and movement. All aspects of life are inherently irregular, like a stream of water.  While on the macro-scale it may appear  as if some manifestations of life  are symmetric and regular, on the micro-scale, symmetry and regularity are meaningless.  Most CAs in Wolfram’s book are symmetric  and  do not move. As they evolve, their  width may vary yet their center of gravity does not.  Even the most complex structures in Wolfram's book  barely scratch the real complexity of life.  Their fabric is made of geometric structures, like triangles, yet  life defies any geometry, even fractal, since it streams


Wolfram proposes several ways to implement movement: In Mobile Automata (p. 71) movement is achieved by updating cells in sequential steps, and not in parallel. In Substitution Systems  (p.82). Elements are replaced by blocks, and the CA expands sideways. In Tag Systems  (p. 93) some elements at one side are removed, and the CA moves sideways.  All these are inadequate for simulating  life in which processes continually interact and are updated in parallel.

Want to simulate life?  Start with a stream.

Still, these arguments  do not contradict Wolfram's main message, that programs simulating complex systems, even life, need not be complex. Yet not all CAs are equally suitable for simulating life. You cannot start with a symmetric CA and hope to simulate a stream. Symmetry and regularity have to be banished from all levels.


Life  creativity  is driven by death, which has to be implemented  at all levels of an emerging artificial structure, like the CAs depicted in previous chapters.

The image below  depicts three CAs. The  CA#600 on the left is symmetric and regular, and does not move.  Its neighbor implements a death mechanism which removes cells in an irregular manner. It is a deterministic irregularity. Whenever a zygote of this CA is planted it will evolve in the same way. One might generate irregularities with random numbers like in Wolfram's book  (p.232). Yet despite their variability, processes in the body  are not at all random, they evolve along predetermined channels, like a zygote which evolves into a human.

In the third CA,  cell death destroys any regularity, and endows the CA with movement. And yet this variability is deterministic.

The graph depicts  centers  of gravity of the first and the third CA. Their zygotes were planted at location 50. While the first CA maintains an invariant position, the other drifts away.

Want to simulate a stream?  Start with a candle.

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