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Fractal
Tree
by
ilyas usal
The following animation is the fractal tree that combines everything about
recursion you have learned until this point:
[ a fractal tree ]
All right, so we have a pretty good start. The last thing we
need to change to get a nice tree is the fact that each branch can spawn a bunch
of baby branches. We are going to take care of that in a nice little for loop.
/*** Constants ***/
sub_branch =
3;
sub_angle = Math.PI/3;
max_size = 7;
branch_length = 50;
branch_length_dimin = .8;
/*** Function ***/
function makeBranch ( start_x, start_y, length, angle, size ) {
if ( size > 0 ) {
this.lineStyle ( size, 0x333333, 100 ) ;
this.moveTo ( start_x, start_y ) ;
var end_x = start_x + length * Math.cos ( angle ) ;
var end_y = start_y + length * Math.sin ( angle ) ;
this.lineTo (end_x, end_y) ;
if (sub_branch >
1) var inc_angle = sub_angle / (sub_branch - 1) ;
for ( var i=0; i < sub_branch; i++ ) {
var newLength = length *
branch_length_dimin;
var newAngle = angle -
sub_angle / 2 + i * inc_angle;
var newSize = size - 1 ;
makeBranch ( end_x, end_y, newLength, newAngle, newSize) ;
}
}
}
/*** Function call ***/
makeBranch ( 200, 200,
branch_length, -Math.PI/2,
max_size);
So, what did we do? First we defined a bunch of variables to edit the code
more easily:
- sub_branch
number of sub-branches. We use that number in the for loop that creates
the sub-branches
- sub_angle
maximum angle that the baby clips will be pointing to
- max_size
size of the tree, that is to say number of recursions, or branches
- branch_length
starting length of a branch
- branch_length_dimin
shrinking ratio of the baby branches
First we substituted those variables in the code to get something a bit more
dynamic. That way, you can change a single variable to get a totally different
tree.
if (sub_branch > 1) var inc_angle =
sub_angle / (sub_branch - 1)
If we have more than 1 sub-branch, we calculate what I called inc_angle,
which is the difference of angle between 2 sub-branches. It's a bit tricky, but
you don't really need to understand it, just trust me. Then instead of creating
one single sub-branch, we create as many as we want with a for loop.
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Ilyas Usal
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