The Algorithmic Beauty of Plants (1990) | Hacker News Reader

The Algorithmic Beauty of Plants (1990)

algorithmicbotany.org

206 pointsingve22 comments

This is one of the trio of great books that Springer Verlag produced around the same time. The other two are The Science of Fractal Images and Beauty of Fractals.

https://www.springer.com/gp/book/9781461283492

https://www.springer.com/gp/book/9783540158516

Two other books that I think are good (but which are for general audiences) are AK Dewdney's Magic Machine which has a chapter about L Systems: https://www.amazon.com/Magic-Machine-Handbook-Computer-Sorce...

And Computers, Pattern, Chaos, and Beauty by Clifford Pickover: https://www.amazon.com/Computers-Pattern-Beauty-Clifford-Pic...

I have work in Beauty of Fractals, I was 18, a fresh faced Midwest geeky punker that got his mind blown by participating in a "math research program" operating out the of Boston University Graphics Lab. It seemed like nonsense, tracking computations with trigonometry functions given imaginary numbers, but the images: this was the first time many of the easily recognized fractal shapes were ever seen. Mandelbrot and DeVanney knew the imagery would be complex interesting, but did not expect the fantastic fractals we all know now. Fun times, indeed.

This is an amazing comment and I would really like to read more if you ever have time to write something up!

Your comment prompted me to do some web searching for documents from our work. Here's a YouTube video of a presentation/lecture we made at the B.U Graphics Lab then, with one of our first rendered fractal animations at the 2:30 mark. I remember working on this. We had AED graphics terminals (able to display 256 colors!) connected to an IBM 3090 mainframe. With special priority, our processes calculating a fractal would only require a few minutes per frame at 256x256 resolution.

https://www.youtube.com/watch?v=6QIhaDvTHXk

I fucked up once, trying to create a 256x256x256 fractal volume. How we were calculating them then was not optimized, and the hardware then is a fraction of the phone you own, and that hardware then was shared across the entire university... After my priority process calculating that 3D fractal volume was killed, because it ground the entire University Computing Center to a halt, the post mortem calculated how long the process would have required: 36 years. It would not be done yet if left running. Oops.

The Computational Beauty of Nature (published by MIT) belongs on anyone's list as well. It walks instructively through several different kinds of complex systems, including L systems, agents (Boids), cellular automata, fractals, chaotic attractors...

Na, the Lindenmayer book was much better. I own them all, and even assisted the authors at a conference where we invited all those fractal heros then. Benoit's book is the very best of these.

It inspired me to produce lots of AutoLisp for the algorithmic simplicity of city planning or architecture. Simple recursive rewriting systems. The problem starts when you need to detect 2d or 3d patterns, and expand them within the steps. This example showed that you only need 1d to create 3d and more. Simply expand the dimensions at the end.

Thanks! I just ordered "The Algorithmic Beauty of Plants" after reading the OP then saw your comments. Would you recommend one of these more than the others?

It's worth looking at ahem unauthorised versions before buying, just to check what they're like.

The Beauty of Fractals contains a lot of colour plates with images that were remarkable for 1986. There's plenty of math on every page. (It really crams a lot of math in).

The Science of Fractal Images is a bit longer. It has fewer colour plates. There's a bit less math (or maybe it's just spread out a bit more?) and there are some pseudo-code descriptions of algorithms.

The other two are much lighter. AK Dewdney's books were aimed at general readers of Scientific American who had access to a home computer. Computers, Pattern Chaos, and Beauty is eclectic. There's some math, and plenty of pseudocode examples.

Being honest: I don't know how well they've aged. Other people might have better descriptions, or alternative suggestions?

Very helpful, thank you!

Dr. P produced the Algorithmic Beauty of Plants while at the University of Regina in Saskatchewan from '82 through '91.

It was published in 1990. I started as an undergrad at the U of R in '88 and eventually completed a MSc in Computer Science there. While I was never directly a student of Dr. P, he left behind a nice lab with a few Silicon Graphics Personal IRIS machines.

I'm 51 now and have had, what I feel, is a pretty successful career. I've worked on animated films, visual effects for films and video games in Los Angeles, New Zealand and in Bellevue, WA.

The allure of those SGI machines in the late '80s is what got me interested in computer graphics. I was never interested specifically in L-Systems, but I have to thank Dr. P as his work led me to where I am. I also must thank my advisor Dr. Xue Dong Yang.

It was a great place to be. A fellow student from that era at the U of R just did an AMA on Reddit.

https://www.reddit.com/r/IAmA/comments/kfpjhg/i_am_dave_plum...

This book has been a favorite of mine for a long time. L-Systems have always fascinated me.

Last spring* quarantine I splurged and finally got a Houdini license. (There’s also a free learning edition with watermarks.) Houdini has a full featured L-System which is compatible with the systems described in this book.

You can even animate the parameters to create cool “growth” animations. Here’s a quick exploration I made recently:

https://www.instagram.com/reel/CIgv8XKJkRx/?igshid=3ixzkhu2t...

(Apologies to non JS / non-Instagram users; only link I have at the moment.)

Correction: originally wrote “last year” when I mean to write “last spring”.

> Last year during spring quarantine I splurged and finally got a Houdini license.

Completely off-topic, butyou made me curious - do you mean this year, or was there some quarantine event last year as well?

Thanks for catching that. No, just an early morning typo before coffee has kicked in :) I meant to write “last spring” not “last year” - though I guess in about two weeks either would be correct.

For anyone not quite ready to splurge, but who wants to try 3D L-Systems, a combination of Blender and the Animation Nodes addon is a free and open source alternative.

My attention was drawn by the following explanation of the Front cover design: The roses in the foreground (Roses by D. R. Fowler, J. Hanan and P. Prusinkiewicz [1990]) were modeled using L-systems. Distributed ray-tracing with one extended light source was used to simulate depth of field. The roses were placed on a background image (photgraphy by G. Rossbach), which was scanned digitally and post-processed.

Computation has evolved quite a lot in 30 years, which makes it even more magical how Prusinkiewicz imagined these wonderful concepts. By the way, does somebody else also wonder why his wikipedia entry doesn't mention a birth year?

I loved this book! Got it out of the library a bunch of times (which shows my age, I guess) and I implemented a few of the algorithms described.

Pairs well with Ken Musgrave’s work on fractal landscape generation.

If curious see also

10 months ago https://news.ycombinator.com/item?id=22248239

2019 https://news.ycombinator.com/item?id=20893196 (1 comment)

2014 https://news.ycombinator.com/item?id=8723728

If you’ve never seen the prints of Ernst Haeckel, they are highly worth perusing (personally I think they are masterpieces):

https://archive.org/details/KunstformenDerNaturErnstHaeckel/...

Great book, I have a first edition.

There is a fairly direct successor I also have called The Algorithmic Beauty of Sea Shells by Hans Meinhardt (Springer-Verlog 1995) which is also full of L-system goodness.

Przemysław Prusinkiewicz is also a contributor to that volume, although not being botany it doesn’t show up in the list linked above.

A friend of mine created this awesome leaf awhile ago: https://web.archive.org/web/20160410210611/http://forum.arbu...

Thanks for the post! I just spent a very enjoyable bit of time on the first chapter of this book.

The people behind that website would love monkey puzzle trees.

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