Background

An honours thesis based on an investigation into modelling the growth of filamentous microbes using Lindenmayer systems was submitted by Fran Soddell to La Trobe University, Bendigo in 1993.

This thesis showed that it was possible to model microbial growth, producing "trees" that resembled colonies of growing microbes. The investigation also collected growth data on a live fungus, Mucor M41, and used these data to produce parametric L-systems to represent Mucor growth.

This page presents 2 models and the resulting sound files produced by Lsys2midi.

This work resulted in a paper presented at the 1994 Complex Systems conference in Townsville, Australia. and published as:

• Soddell F, Seviour RJ & Soddell J (1994). Using Lindenmayer systems to investigate how filamentous fungi may produce round colonies. pp 61-68. In: Complex Systems: Mechanisms of Adaptation eds Stonier, R, Xing Huo Yu. IOS Press: Amsterdam.
• The paper was also published in Complexity International, Vol 2

Dichotomous branching (branches at growing tip) occurs occasionally in fungi

L-system
/* * Fran Soddell * honours thesis fig 17 * fig17g * altered to make music * Date:11/01/00 */
#define maxgen 11
#define step 0.25
#define delta 25
START : F(step)b
p1: b -> [+(delta)F(step)b][-(delta)F(step)b]

F17 MIDI file
F17organ excerpt
F17db excerpt
F17goa excerpt

The midi file presented here represents the output from generation 12 using a general midi organ as the default instrument. The midi file contains 2 parallel sequences generated by the L-system, but differing by the defaults used in lsys2midi (different starting note and different range). The file produced some interesting "systems music" when used with different instruments. Presented here are excerpts using an XG organ. and three excerpt generated by the same midi file (generation 8 this time) using XG organs, a percussion patch on the cs1x synth and a goa trance track (with added beats not produced by the L-system). The piece called mycobeat uses the same MIDI sequence

F17slow MIDI file

The L-system above could be modified by changing the step length to show changes in growth rate of the organisms. This resulted in the same image, but the change in growth rate could be detected by changes in tempo.

Lateral branching (branches away from growing tip) is commonly found in fungi

L system
/* * Fran Soddell * honours thesis fig 16 * fig16 * altered to make music * 11/01/00 */
#define maxgen 7
#define step 0.5
#define delta 25
START : F(step)b
p1: b -> [+(delta)F(step)b]F(step)a
p2: a -> [-(delta)F(step)b]F(step)b

F16 and F17 MIDI file combined

The L-system for dichotomous branching sounded similar to the L-system for lateral branching. Since it was difficult to tell the difference on casual listening we created a midi file that contain one dichotomous and one branching L-system. Can hear there are differences.

Stochastic systems
each run is different

F24both MIDI file

Every time a stochastic L-system is run, the output is different because of the random rules. This example contains two sequences derived from different runs of the same system. See the stochastic example in what are L-systems for the L-system for this file.