There is also "The Algorithmic Beauty of Seaweeds, Sponges and Corals" (https://link.springer.com/book/10.1007/978-3-662-04339-4), and, my personal favorite in the series, "The Algorithmic Beauty of Sea shells" (https://link.springer.com/book/10.1007/978-3-540-92142-4).

I really enjoyed reading the latter last year, because it does a great job slowly building up. By the end, I felt like I didn't just understand the models, but also how the author found them. I can recognize these patterns in nature, and figure out how they were generated.

I spent some time last year implementing all the models described in the book in JS: https://kaesve.nl/projects/shells .

Grabbing the wheel and jerking hard left, some of the gradients when my browser rendered the gallery we very optical illusion-y. I could have sworn the lines were animated, to the point I moved my cursor to the end of a line to see it was not moving.

playing around with the parameters of your interactive sea shell model, I got these other beautiful shapes which then made me wonder how come there wasn't some random mutation in their generation in nature in the past to make them look that way, and then I realize survival is the name of the game, and these natural object could have been that shape at one point in history but didn't make it through for us to see them... though more I think, some of their fossils should have remained....

https://github.com/bmitc/fsharp-science-and-math-notebooks/b...

I have had the book for years but recently started properly going through it with F# inside a Polyglot Notebook. I have all the 2D diagrams drawn up until the book starts with the stochastic drawings, which I'll tackle next. F# makes it so nice to build an embedded DSL for the L-systems and then the turtle interpretation of them.

    // Figure 1.9 (d)
    let kochD =
        { Alphabet = ['F'; 'f'; '+'; '-']
          Axiom = "F-F-F-F"
          Productions =
            [ 'F' => "FF-F--F-F" ] }

    drawTurtleSystem 4 defaultTurtle kochD

I'm not sure what I'm going to do with the 3D drawings. There may be a way in the Polyglot Notebook to have F# emit WebGL or something.

D'Arcy Thompson: https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson

https://en.wikipedia.org/wiki/On_Growth_and_Form (1917)

in the pdf:

Thus, self-similarity in plants is a result of developmental processes. Growth and form By emphasizing the relationship between growth and form, this book follows a long tradition in biology. D’Arcy Thompson [143] traces its origins to the late seventeenth century, and comments: Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space.

Can you help me unpack the distinction between an event in space-time vs merely a configuration in space?

Growth is driven by hormone flow in cells and organs. It doesn't have to distribute equally. And, it's intensity and duration affects rate and extent of growth. Cells have primitive clocks. (Rhythms) - so there is a cyclical, flow, time and distance function. Plus gravity. Some hormones inhibit growth. Some encourage. Some intensify expression under light, some inhibit. Some head down. Some head up.

Rapid growth vs slow growth. Directional growth vs directionless. Stages of growth are different, time has consequences. If you only consider space you ignore the consequences of time. Think about abcission cells, how plants shed leaves, fruit, how horns can fall off.

(This is from memory of 40 year old biology lessons at uni)

How could you have time without space? They're kind of equivalent in my conceptual model. I think of both time and space as a sine wave. The way you expressed it actually matches that for me. Thanks for sharing!

I love it when computer science, programming, or anything tech related gets related with other disciplines. Botony + Algo(Math?) = Beauty

Apropos, https://github.com/two-twelve/fernery a "tool for generating images of ferns and other Iterated Function Systems" was recently posted somewhere

Great book! Back in my cs study days, I did a project based on this book about lindenmeyer systems and fractals: https://lsystems.raphaelpour.de/