Each point on the image plane defines a ray through that point starting at the
camera. The ray caster then samples the frustum along this ray starting from
the image plane. Before iterating the map the points are transformed as outlined
in section . The transformed point is then iterated with the map *q*^{2}+*c*.
If the point is within distance 2 of the origin after reaching the maximum
number of iterations it is considered to be bounded and therefore inside the
fractal. Points are sampled until either the far plane is hit or two points
bounding the surface are found. In that case a binary search is done to locate
the surface more precisely.

`compute_depths()`

` foreach pixel`

` point = pixel;`

` while(point < far_plane)`

` if(sample(transform(point)))`

` refine_surface(point);`

` break;`

` else`

` point += step;`

` depth[pixel] = point - pixel;`

`refine_surface()`

` for i=0 to num_adaptave_iterations`

` step_size /= 2;`

` if(outside(sample(transform(point))))`

` point += step_size;`

` else`

` point -= step_size;`

This step of the algorithm is parallelized by scanline, with an arbitrary number of threads computing scanlines in parallel.