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Fractint L-Systems Definition

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A tutorial by William McWorter

* mcworter@midohio.net *

version 1.4

January 1997

Back to Tutorial Index

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WHAT ARE L-SYSTEMS

An L-system is an automaton designed by Aristid Lindenmayer in 1968 to model
cell development. Cells are represented by symbols and cell subdivision is
modeled by replacing these symbols with strings of symbols. Here is a simple
L-system with two cell types represented by the letters A and B. Cell A
subdivides into two cells represented by the string AB. Cell B subdivides
into two cells represented by the string BA. The ordering of the symbols is
relevant in an L-system. The abstract organism this L-system models grows by
repeated cell subdivision. At birth the organism is the single cell A. After
one subdivision the organism is two cells represented by the string AB. After
two subdivisions, each cell subdividing according to the subdivision rules
above, the organism has four cells given by the string ABBA. After three
subdivisions the organism is represented by the string ABBABAAB and after four
subdivisions the organism has 16 cells represented by the string
ABBABAABBAABABBA.

FRACTINT requires this information in separate lines of text in the form:

Thue { ; The L-system's name followed by "{"
; to signal the beginning of its description
Axiom A ; Provide the birth string for the organism
A=AB ; Give the replacement string for the cell A
B=BA ; Give the replacement string for the cell B
} ; Signal the end of the organism's description with a "}"

The order of an L-system is the number of times cell subdivision occurs.

Of course all this is meaningless unless the symbols are interpreted in some
way. This particular L-system is given a mathematical meaning in an article
by Cobham in Mathematical Systems Theory, Vol. 6, 1972, pp. 164-192. This
article also investigates mathematical properties of L-systems in general.

FRACTINT regards each symbol as a graphic command. FRACTINT reads the symbol
string from left to right executing a command for each symbol it encounters.

L-systems as interpreted by FRACTINT can be very striking and complex. Many
examples will be given here of tilings, space-filling curves, and plant
simulations. Let's begin with modeling plants.

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