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The algorithmic beauty of plants (1990)

de Przemyslaw Prusinkiewicz, Aristid Lindenmayer

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The beauty of plants has attracted the attention of mathematicians for Mathematics centuries. Conspicuous geometric features such as the bilateral sym?? and beauty metry of leaves, the rotational symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most exten?? sively. This focus is reflected in a quotation from Weyl [159, page 3], "Beauty is bound up with symmetry. " This book explores two other factors that organize plant structures and therefore contribute to their beauty. The first is the elegance and relative simplicity of developmental algorithms, that is, the rules which describe plant development in time. The second is self-similarity, char?? acterized by Mandelbrot [95, page 34] as follows: When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. This corresponds with the biological phenomenon described by Herman, Lindenmayer and Rozenberg [61]: In many growth processes of living organisms, especially of plants, regularly repeated appearances of certain multicel?? lular structures are readily noticeable. . . . In the case of a compound leaf, for instance, some of the lobes (or leaflets), which are parts of a leaf at an advanced stage, have the same shape as the whole leaf has at an earlier stage. Thus, self-similarity in plants is a result of developmental processes. Growth and By emphasizing the relationship between growth and form, this book form follows a long tradition in biology.… (mais)
Adicionado recentemente porAriaMK, NorpchenSparks, nullset, zhuazhua88, colinsebestyen
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A whole book about L-systems! Wow!
  themulhern | Apr 24, 2022 |
This... was a somewhat unepxected read.

Essentially, it's a textbook about how Lindenmayer systems (L-Systems) can be used to simulate and model plants in increasingly complicated ways.

In a nutshell, L-Systems are a series of rewriting rules that are applied over and over again. For example:



Figure a shows that if you replace `F` with `F[ F]F[-F]F`, where `F` means draw a line, `[` and `]` control branches, and ` ` and `-` branch left and right, that alone is enough to give you that nice branching structure. the same for the other more complicated patterns.

They do get more complicated from there, including things like parameters (`F(1)` is move forward one, otherwise you can rotate by various angles that changes as you go along):



You can even get into full 3D models:



It's kind of amazing how relatively accurately you can model all sorts of plants and even simple animal cells with this. And this book goes a long way towards building this up for you.

All that being said, it does get very very mathy at times:



It's the sort of thing that I love, but you really should remember: this is a textbook. It reads like one. I wonder if there are any online classes to follow along using this book. Something work looking at.

In any case, if you're looking for a textbook about how L-Systems can model plants and just how complicated L-Systems can get (while still maintaining their 'order from a few short rules'), this is a great book. Well worth the read.


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  jpv0 | Jul 21, 2021 |
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The beauty of plants has attracted the attention of mathematicians for Mathematics centuries. Conspicuous geometric features such as the bilateral sym?? and beauty metry of leaves, the rotational symmetry of flowers, and the helical arrangements of scales in pine cones have been studied most exten?? sively. This focus is reflected in a quotation from Weyl [159, page 3], "Beauty is bound up with symmetry. " This book explores two other factors that organize plant structures and therefore contribute to their beauty. The first is the elegance and relative simplicity of developmental algorithms, that is, the rules which describe plant development in time. The second is self-similarity, char?? acterized by Mandelbrot [95, page 34] as follows: When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. This corresponds with the biological phenomenon described by Herman, Lindenmayer and Rozenberg [61]: In many growth processes of living organisms, especially of plants, regularly repeated appearances of certain multicel?? lular structures are readily noticeable. . . . In the case of a compound leaf, for instance, some of the lobes (or leaflets), which are parts of a leaf at an advanced stage, have the same shape as the whole leaf has at an earlier stage. Thus, self-similarity in plants is a result of developmental processes. Growth and By emphasizing the relationship between growth and form, this book form follows a long tradition in biology.

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