"ingo" <nomail@nomail> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>
> > [...] I started to
> > rewrite his L-system code to work in POV-Ray v3.7.
> >
>
> I already started wondering about the silence from Norway, but then, as Jack out
> of the box, there is beautiful code. Thank you Tor Olav.

Hi Ingo  :-)

I'm just lurking around in the background. I do not have as much time for
POV-Ray code writing as I once had.

Lately I've been working, slowly, on these two projects - which are not finished
yet:

https://github.com/t-o-k/POV-Ray-matrices
https://github.com/t-o-k/Predynastic-Egyptian-granite-vase

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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"Colin Fleming" <Colin Fleming> wrote:
>...

> Hi Tor,
>
> This is great work!

Thank you Colin


> Przemyslaw Prusinkiewiczs book, "The Algorithmic Beauty of Plants" was one of
> the first books I bought on L-Systems.
>
> If anyone is interested, you can download the book here:
>
> http://algorithmicbotany.org/papers/abop/abop.pdf


Thank you for that link. I did not know that it is freely available.

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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"Droj" <803### [at] drojde> wrote:
> "Droj" <803### [at] drojde> wrote:
>
> > >
> > >   axiom = FX
> > >   X -> >[-FX]+FX
> > >   angle = 40
> > >
> > Yes, this was the one. I had to scratch my head more than once when I used it.
> > It couldn't be symmetric and an angle of 40 could not be right.
> > I usually trust PB a lot but I guess something went wrong during publishing...
> >
>
> Have to correct myself.
> It took some time to figure out how it works but it is symmetric and the angle
> is acceptable, too.
> But his rule means branches grow (>) with each iteration instead getting smaller
> (<).

Those rules can be a bit confusing.

If the scale number is greater than 1, then > will increase the line width and <
will decrease it. And if it is less than 1 the opposite will happen.

It seemed that P.B. had used the golden ratio for the branch width scaling:

phi = (1 + sqrt(5))/2 = 1.618033988749...

So to make the branch radii decrease by their "distance" from the stem when
using the > symbol, I used the reciprocal of phi, i.e. 1/phi = 0.61803398875...

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:

>
> I don't know if this reprint (or new edition ?) "The Fractal Geometry of Nature"
> book by Mandelbrot contains any L-system images/rules:
>
> https://www.amazon.com/Fractal-Geometry-Nature-Benoit-Mandelbrot/dp/1648370403
>
> If so then I'll have to consider buying it.
>

I think the 'The Algorithmic Beauty of Plants'
(http://algorithmicbotany.org/papers/abop/abop.pdf) is a more up-to-date version
of L-Systems.

>
> But I'm not sure how the rules should work in 3D. Have you seen any such
> images with accompanying 3D rules? If so, that would help me understand what is
> needed.
>

It's not too much. 2 symbols for pitch up/pitch down and 2 symbols for roll
left/roll right. And some 'placeholder' chars like A,B,...
See chapter 1.5 in the book I mentioned above.

There is also an axiom and rule for the famous Hilbert curve in 3D and a 3D
bush-like structure including images of both.

The only program that covers 3D L-Systems is Lparser by Laurens Lapre but it's
MS DOS only. But I will rummage through the .LS files to find things we can use.

Cheers, Droj

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"Droj" <803### [at] drojde> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>

> >
> > But I'm not sure how the rules should work in 3D. Have you seen any such
> > images with accompanying 3D rules? If so, that would help me understand what is
> > needed.
> >
>
Hi TOK,

Let's take the example of PB's Pythagoras tree. We can easily use a copy of it
and rotate it 90*y to get a tree with more branches.
But instead we can use your L-system directly and the following axiom/rules:
axiom:
AB
rules:
A = [F[+F<A][-F<A]]
B = [F[^F<B][&F<B]] // rotate
< // l/LengthScale
angle = 45 degrees
The confusing thing is: Lindenmayer's System is a righthanded system and ^ and &
mean pitch up/pitch down.
We are used to the lefthanded system and that means to me: roll left/roll right
in which case we have to use \ and /.

See image generated with L. Lapres Lparser and rendered with Povray.

Here's a link with lots of examples:
https://www.houdinikitchen.net/2019/12/21/how-to-create-l-systems/

Cheers, Droj

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Attachments:
Download 'pyth017.png' (267 KB)

Preview of image 'pyth017.png'

"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:

> I'm just lurking around in the background. I do not have as much time for
> POV-Ray code writing as I once had.

Same here.
You have some nice looking projects there.

ingo

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"Droj" <803### [at] drojde> wrote:

> The only program that covers 3D L-Systems is Lparser by Laurens Lapre but it's
> MS DOS only.

The code of it is available https://github.com/jvail/L-System

A nice one to test stuff: https://jvail.github.io/L-System/

ingo

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hi,

"ingo" <nomail@nomail> wrote:
> ...
> The code of it is available ...

and works, with v little work, on Linux.  liking the VRML output :-).


regards, jr.

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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:

> If so, then I've shown how this can be used without much adaptation in a new
> example in the repository.
>
> Please post some more images made with the axioms and rules that you've
> collected.
>

Hi TOK,

I packed some POV files using your L-system in the archive below to extend your
examples collection.

Cheers, Droj

Post a reply to this message

Attachments:
Download 'tok_l-sytems.zip' (12 KB)

"Droj" <803### [at] drojde> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>
> > If so, then I've shown how this can be used without much adaptation in a new
> > example in the repository.
> >
> > Please post some more images made with the axioms and rules that you've
> > collected.
> >
>
> Hi TOK,
>
> I packed some POV files using your L-system in the archive below to extend your
> examples collection.

Thank you Droj. I'll have a look at it.

I should mention that I have now made a modified version of my L-system library
that can create 3D shapes. - And I've managed to render a 3D Hilbert curve. But
I have not had time do more test.

Now I'm in doubt if I should create a new repository for the 3D version of the
library, or if I should update the existing 2D library, making it more
circumstantial to use.

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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