"Lindenmayer Systems, Fractals, and Plants" (PRUSINKIEWICZ; HANAN, 1989) https://link.springer.com/book/10.1007/978-1-4757-1428-9
![Preface
L-systems are a mathematical formalism which was proposed by Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of development. The notion promptly attracted the attention of computer scientists, who investigated L-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed L-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between L-systems and the concept of fractals introduced by Benoit Mandelbrot. The work by Smith inspired our studies of the application of L-systems to computer graphics. Originally, we were interested in two problems:
• Can L-systems be used as a realistic model of plant species found in nature?
• Can L-systems be applied to generate images of a wide class of fractals?
It turned out that both questions had affirmative answers. Subsequently we found that L-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of 1systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals. [...]](https://media.ciberlandia.pt/ciberlandia-media/media_attachments/files/114/359/648/324/216/418/original/5afad812e0de7c99.png "Preface
L-systems are a mathematical formalism which was proposed by Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of development. The notion promptly attracted the attention of computer scientists, who investigated L-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed L-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between L-systems and the concept of fractals introduced by Benoit Mandelbrot. The work by Smith inspired our studies of the application of L-systems to computer graphics. Originally, we were interested in two problems:
• Can L-systems be used as a realistic model of plant species found in nature?
• Can L-systems be applied to generate images of a wide class of fractals?
It turned out that both questions had affirmative answers. Subsequently we found that L-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of 1systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals. [...]")
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Code at: https://github.com/villares/sketch-a-day/tree/main/2025/sketch_2025_04_05
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Code at: https://github.com/villares/sketch-a-day/tree/main/2025/sketch_2025_04_03
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@liaizon thank you!
If you are curious, I added some references about L-Systems to this post: https://github.com/py5coding/py5generator/discussions/555
#LSystem Code at: https://github.com/villares/sketch-a-day/tree/main/2025/sketch_2025_04_02
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@neauoire @chrisamaphone Have you ever played around with L-Systems (I bet you did :)? It seems there's a lot of conceptual overlap here, even though they don't offer much in terms of control flow or Turing completeness. I just think they generally still remain somewhat under exposed/explored (beyond the traditional Turtle graphics applications). If you attach different kinds of interpreters, they can be pushed pretty far... In the past I have used them for genetic programming, text & code generation, music composition, and even basic stack machines (where the L-System acts as an iterative macro expansion stage)...
A couple of FizzBuzz examples (incl. a super basic Forth-like VM) using https://thi.ng/lsys...
https://gist.github.com/postspectacular/7d0ae7d90e0eafb69e60fb97e2838221
thi.ng/lsysFunctional, extensible L-System architecture w/ support for probabilistic rules
I love to play/create an #LSystem, check discussion at https://github.com/py5coding/py5generator/discussions/555 Code at: https://github.com/villares/sketch-a-day/tree/main/2024/sketch_2024_11_11
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Mathematisch lassen sich komplexe Phänomene oft unerwartet einfach beschreiben. Doch hinter dieser Einfachheit verbergen sich überraschend vielfältige Welten.#KochscheSchneeflocke #Fraktal #Freistetter #FreistettersFormelwelt #AristidLindenmayer #L-System #Mathematik
Freistetters Formelwelt: Die komplexeste Schneeflocke der Welt
Freistetters Formelwelt: Die komplexeste Schneeflocke der Welt
www.spektrum.deFreistetters Formelwelt: Die komplexeste Schneeflocke der WeltMathematisch lassen sich komplexe Phänomene oft unerwartet einfach beschreiben