The structure of patterns

Starting a new chapter, of sorts. I have been researching the structure and patterns of plants. Based on the studies of biologist Lindenmayer the patterns of organic forms are easy to identify, the more the organism grown the more complex the patterns become. Lindenmayer’s systems, or L-systems for short, are also quite popular for the generation of artificial life.

untitled morpheme no1

Round acrylic painting made with the principles of the L-system nature patterns.


​Wood, Acrylic paint.

The recurring pattern of Lindenmayer’s system becomes repetitive, or copying of previous patterns creating fractal shapes and are thereby identify as the L-system.

L-system grammars are very similar to the semi-Thue grammar (see Chomsky hierarchy). L-systems are now commonly known as parametric L systems, defined as a tuple

G = (V, ω, P),


  • V (the alphabet) is a set of symbols containing both elements that can be replaced (variables) and those which cannot be replaced ("constants" or "terminals")

  • ω (start, axiom or initiator) is a string of symbols from V defining the initial state of the system

  • P is a set of production rules or productions defining the way variables can be replaced with combinations of constants and other variables. A production consists of two strings, the predecessor and the successor. For any symbol A which is a member of the set V which does not appear on the left hand side of a production in P, the identity production A → A is assumed; these symbols are called constants or terminals. (See Law of identity).

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