projecttree2D.c

Compute the frontal area of a fractal tree

Compute the frontal area of a fractal tree

A generated fractal tree is projected onto a plane.

Iteratively adding branches

There is an increasing overlap and horizontal orientation of branches.

set logscale xy
set grid
set xlabel 'Branches'
set key box top left
set ylabel 'see key'
plot 'out' u 1:2 t 'Area R^{-2}', '' u 1:3 t 'Length R^{-1}'

Compare area against total branch length (script)

reset
set logscale xy
set grid
set xlabel 'length R^{-1}'
set ylabel 'area R^{-2}'
set key top left
plot 'out' u 3:2 t 'data', 5*x**0.62 w l t '0.62 scaling'

(script)

#include "grid/cartesian.h"
#include "treegen.h"
#include "utils.h"

Branch * trees;
scalar f[];
face vector fs[];

int main() {
  L0 = 50;
  X0 = -25;
  N = 400;
  init_grid (N);
  srand(0.);
  double angle = -pi/2.; //Rotate tree
  levels = 3;
  trees = tree_skeleton();
  double tl[nb];
  for (int j = 0; j < nb; j++) {
    coord strt = trees[j].start;
    coord end = trees[j].end;
    double bl = 0;
    foreach_dimension(3)
      bl += sq(strt.x - end.x);
    if (j > 0)
      tl[j] = tl[j - 1] + sqrt(bl);
    else
      tl[0] = sqrt(bl);
    trees[j].start.x = cos(angle)*strt.x - sin(angle)*strt.z;
    trees[j].start.z = 0;
    trees[j].end.x = cos(angle)*end.x - sin(angle)*end.z;
    trees[j].end.z = 0;
  }
  int nt = nb;
  
  for (nb = 1; nb <= nt; nb++) {
    tree_interface (trees, f, fs);
    double A = 0;
    foreach() 
      A += dv()*(1 - f[]);
    printf ("%d %g %g\n",nb, A, tl[nb -1]);
    output_ppm (f, file = "c.mp4", opt = "-r 3");
  }
  free (trees);
}