Branching poisson disk algorithm

My program outputs a distribution like this:

Every dot is at least a distance of 10 pixels from any other.
The way it works is to start at the middle, and branch out in 3 evenly spaced directions at a random angle from the center dot, then from those 3 points branch in a similar way generating more points and continue in that fashion for a certain number of iterations, above is 25 generations. I think this picture helps explain it a lot.

The speed is fairly quick, generating these graphs in python took only about 1.5 seconds for around 1300 points, I think it could be speeded up considerally using parallel processing for example on a gpu with a faster language. 

**Python source code**
import math
import random
import Image, ImageDraw
def check(d, pointlist, point, gridsize):
    tooclose = False
    if point[0] < 10 or point[0] > gridsize[0]-10 or point[1] < 10 or point[1] > gridsize[1]-10:
        return True
    for p in range(0, len(pointlist)):
        if ((point[0]-pointlist[p][0])**2.0 + (point[1]-pointlist[p][1])**2.0)**.5 < d-1:
            return True
    return tooclose
def findspot(pointlist, added, d, gridsize, draw):
    newlist = []
    newadded =[]
    for point in pointlist:
        newlist.append(point)
    for point in added:
        tx = point[0]
        ty = point[1]
        theta = random.random()*2*3.14159
        for i in range(0, 3):
            px = tx + d*math.cos(theta+i*(2*3.14159)/3)
            py = ty + d*math.sin(theta+i*(2*3.14159)/3)
            if check(d, newlist, [px,py], gridsize) == False:
                newlist.append([px,py])
                newadded.append([px,py])
    return newlist, newadded
class graph():
    def __init__(this, d, gridsize, draw):
        this.pointlist = [[400,400]]
        this.added = [[400,400]]
        this.d = d
        this.gridsize = gridsize
        this.draw = draw
    def tree(this, limit):
        newlist, newadded = findspot(this.pointlist,this.added,this.d, this.gridsize, this.draw)
        if limit < 25:
            this.pointlist = newlist
            this.added = newadded
            this.tree(limit+1)
def main():
    gridsize = [790,790]
    d = 10.0
    point = [400,400]
    plot = Image.new("RGB", [800,800])
    draw = ImageDraw.Draw(plot)
    G = graph(d, gridsize, draw)
    G.tree(0)
    for point in G.pointlist:
        for i in range(-1, 2):
            for j in range(-1, 2):
                plot.putpixel((int(point[0]+i), int(point[1])+j), (255,255,255))
    plot.save("plotdot.png")
main()