Identify rules for fractal L-system for plant representation using lengths and angles

[netpumber]

As some of you already knew, to develop an L-system fractal you need some rules for angles and lengths. L-system also is well known for its application in plants. So i had a plant in the ground and measure the lengths(cm) of branches and their angles. For example i will post some of the data here.

Lengths (cm): Beginning from the bottom and going upwards.

1st generation)                                              64

2nd generation)                    31,8                    |                            20,1

3rd generation)               19,3 | 22,6                |                         25 | 25,8

4th generation)         7,7|23,6 | 21,4|12,2        |                  17 | 19 | 22 | 5

and so on... its a little chaotic to write it all here.

Angles: Beginning from the bottom and going upwards.

1st generation)                                     36

2nd generation)               38                  |                  41,9

3rd generation)    30,7      |    32,2         |      30          |      45,7

4th generation) 27,5|25,2 | 42,9| 28,7   |   31,6|         |     39|

The question is if its possible to represent that plant with those features as an L-system and how can i determine the rules of that system.

Thank you.

[tar]

neptumber,

 

I did not know what an L system fractal was until a half hour ago, so I probably am not one of the parties to whom you addressed this question, but my guess is the answer is, yes you can, and determine the rules, by describing what happens at each branch.

 

I believe this guess is correct because the plant formed by following a particular rule at each node. This is probably constrained by geometries and the crystal shapes of the elements which compose the plant. Primarily carbon, as carbon is the base element of carbon based life. The general form of the carbon ring is a hexagon, which you will find many of in any organic chemisty book. Also, by noting the 4 intersecting hexagonal planes defined by the cubic octahedron, or the spherical rhombic dodecahedron, you might make a good guess that space is liable to be laid out in a manner, and a plant is liable to make a rule based decision at a branch point, based on a hexagonal notation. Angles like 45, 90, 120 and 60 and close multiples and divisions of such, would therefore not be surprising to find in the plant, and thusly in your rules. In terms of your notation, in determining a string of characters to describe the rule, I have an untried hypothesis that you might be able to use a system I came up with last month. The system includes a two letter notation for each of the twelve general directions that a branch could take. (actually 11 usable directions, since the stem just came from one.) The notation would have to doctored up a bit, for your purposes, since I used colors and capital and small letters, but you could use the alternate method of just labeling each of the distinct twelve directions as 1,2,3,4,5,6,7,8,9,10,11, and 12, or A,B,C,D,E,F,G,H,I,J,K and L, or if its ok to consider r and R different characters, RY, RG, Br, yr, gr, Rb, gY, yb, yG, BY, BG, and gb.

 

As you can see, each letter appears exactly 6 times, discribing its own hexagonal plane, so the notation system is clean an meaningful.

For your distances you have the cms and you can drop the angles and replace them with the direction in which the branch goes.

 

Might work out. Or you might be able to massage the scheme to fit your purposes.

 

Regards, TAR