L-System plants
This page describes two programs (really one), which recursively draw lsystem
plants.
The procedure is as follows:
-
Define the number of new branches to draw at each stage
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Define the number of times to call the recursive branch drawing function
(number of orders)
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For each branch, define the angle, it leaves the parent from, how much
shorter it is (as a fraction of the parent length), and at what fraction
along the parent's length it branches
-
Draw the trunk (vertical)
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For each order, draw each branch with the desired attributes, attached
to the parent
-
Draw new branches on each newly created branch
-
Continue to do this until the correct number of recursions have taken place.
For example, using the first program, the following parameters are entered:
One branch, three orders,
Branch one: -30 degrees, 0.5 times as long as the parent, and branching
0.5 of the way along the parent
This produces the following image:
Note how there are 3 branches (and a red trunk). This corresponds to the
3 orders. The brownish branch is drawn 0.5 of the way along the trunk,
and is 0.5 times as long. It emerges at -30 degrees (11 o' clock position).
Next consider the following:
Two branches, three orders
Branch one:-30 degrees, 0.5 length, 0.5 ratio
Branch two:50 degrees, 0.5 length, 0.5 ratio
Notice now how there are two branches leaving the trunk, and two more leaving
each of those, and two more leaving each of those (14 in total).
Using the 'random stuff' feature causes the computer to randomly pick
the angle, length, and ratio for each branch. (instead of typing it in).
The seed allows you to recreate the same random tree again.
Warning: Total number of twigs drawn increases exponentially with the
number of orders - for 3 branches and 4 orders there are 120 twigs, for
3 branches and 5 orders there are 363. So using several branches can quickly
cause an unacceptable drawing time. Anyway, it just ends up producing a
messy spiky bush anyway!
The second program just varies the three parameters using sine waves
(frequencies determined randomly with a seed), and uses the keys to smoothly
vary the parameters (either slowly or quickly). This quickly allows creation
of realistic bushes, simply by cycling through many similar sets of parameters.
The screenshots show some examples. Best results are obtained just
be messing around.
Qbasic l-system plants program
Qbasic l-system animated plants program
Screen shots (Parameters as shown)
