Iteretív grafika=fractal

Take a series of bars and construct an arrangement with the following algorithm: Align a bar vertically to from the stem. Put two bars on top of the stem, which will be representing the left and right branches. Now we have a unit of three bars. Start the construction again: align again a bar vertically to form the stem again. Now reduce the size of the first unit and place it on the top of the stem as the right branch. Let the left branch be the former right branch. Now we can start all over again: align a bar vertically as a stem, etc.
Observe that the quantity of branches corresponds to successive Fibonacci numbers.


2
1+2=3
2+3=5
3+5=8
Now that we have a special arrangement of bars, which can be called as a Fibonacci tree, let us start to give him/her instructions how to become a real tree.
Let us now decrease the branching angle gradually. Easy does it.

This is what happens when the angle of one branch is zero degree, and the angle of the other branch is 90 degrees.
How would a tree look like if branches were grown on one side only?
Until now our tree grew in a single plane. Sometimes, trees also grow in three dimensions, for instance with a twist of 90 degrees at each successive branching (if a tree intends to become a TV antenna).
See LiveGraphics3D: f8
Trees like to hide regularity, if it is too evident. For this reason they tend to develop branches in every direction, although they usually maintain the same branching angles and the twisting angles at the branching (what a trick).
See LiveGraphics3D: g8a
This should be enough for a tree to know how to grow, however, for sophisticated trees some additionally details should also be controlled.
Trees should be cautioned to reduce the size of the successive branches gradually. A reduction exceeding 60 % is too much for sure (one should be careful of the appearance), while a reduction not exceeding 10 % would not do either (the principle of ensuring equal strength along the way is not complied with, and the available space is often limited).

Why not try the good old extreme and mean value, and chose a reduction of about 22 %.


It is also worth to know that no living organism is perfect without some imperfection. Grow some branches from the mid section.
And finally, let us have a closer look to check how the birds would like it.
Just a moment, before you start to grow all over the place without proper control: produce some useful fruit, otherwise you will be cut down in no time. Cubes are greatly recommended, but spheres are not so bad either.