Lsystem phyllotaxis

[danilo2]

Hi!

I'm trying to make Lsystem, which places elements in circle phyllotaxis.

I've managed to do it, with formula:

Premise: -X(1)

Rule1: X(h) = +f(0.1*h^0.5)JX(h+1)

And I'm really very long searching for rules, which descibes thesame phylotaxis, but with elements, which are smaller inside and larger outside (of course the problem is not with getting these elements bigger, but with spaces between them - I want that smaller elements in the middle have the same spaces between each other as larger elements), as we can see for example in attached image.

Thank you very much!

[danilo2]

the image:

Edited April 19, 2010 by danilo2

[Macha]

It's a start.

lsys.hipnc

[danilo2]

It's a start.

Thank you very much!

I didn't thought,that solution of this problem is so simple!

Thank you once again!

[dyei nightmare]

this is a very very interesting topic, the sunflower pattern

and this

[danilo2]

Yes it is

The sunflower pattern could be done with Macha's rule,

but I'm wondering if anybody knows the rule of spherical phyllotaxis - placement of objects, eqal size in eqal distances from each other on sphere?

It would be great if somebody knows it!

[Macha]

Despite the sphere equation below, the LSystem solution eludes me. I can make romanesco cabbages though. By the way, I picked one of those up the other week while coming back from a mountain walk and they are very nice, like broccoli but softer.

romanesco.hipnc

Edited April 21, 2010 by Macha

[michael]

nice examples Macha

but if you had paid attention to the front page and seen this you'd know that the proper angle is 137.5...!

http://odforce.net/2010/04/07/nature-by-numbers

[Macha]

but if you had paid attention to the front page and seen this you'd know that the proper angle is 137.5...!

Hehe, yes I was aware of this value but I took it to be non essential. Any range of numbers will actually work and I bet there is quite some variability in those plants that exhibit "true" Fibonacci sequences.

Edited April 22, 2010 by Macha