@MISC{_blocksubstitution,,

author = {},

title = {Block Substitution, Part 1: Basic Concepts},

year = {}

}

Intuition tells us that it takes a complex system to produce complex results. This intuition turns out to be incorrect: Very complex results can be produced by simple systems in which simple rules are applied repeatedly and in parallel [1]. This phenomenon is seen in drawdown automata [2] and L-Systems [3, 4]. This article describes another kind of system in which complex patterns can be produced by applying very simple rules over and over again. The technique is called block substitution [1]. This example dramatically illustrates that complex and surprising patterns can result from the repeated application of the simplest of rules. Block substitution systems by their nature produce fractal patterns. For the example above, this can be seen by the development of the patterns through successive iterations: The Block Substitution Process In block substitution systems, pattern are considered to be composed of cells of various colors. A (usually) small block of cells is associated with each color. For one iteration of block substitution, every cell in the pattern is replaced by its corresponding substitution block. This is where parallelism comes in. The process then is repeated. As the result of successive iterations, the original pattern grows larger and (usually) more complex. Here is a simple example. There are two colors, black and white. The substitutions rules are The process starts with a single black cell. Here is the pattern that results after five iterations: As block substitution rules are iterated, the pattern grows larger and larger — doubling in dimensions for 2 × 2 substitution blocks with each

block substitution basic concept successive iteration simple rule complex result block substitution system substitution block drawdown automaton simple system repeated application surprising pattern corresponding substitution block original pattern grows simple example complex system small block complex pattern various color fractal pattern block substitution rule single black cell block substitution process substitution rule

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