I don't see why it should throw this error, as you don't even have a function in your code.
Which is excessively slow!
point() is really the slower part of it, but even if I remove its call (it can be replaced with pixels[] array usage), it is slooow...
The issue might be in computing pow() so many times. We can already collapse the two identical loops into one.

I see, I guess point() is very slow because you are doing lot of drawing outside the sketch area itself...
Here is a version completing in a reasonable time, without stack overflow.
size(750, 800);
background(0);
smooth();
stroke(255);

int my = height / 3 * 2;
int seed = 5;
randomSeed(seed);
float axeY = 0;
float axeX = 0;

loadPixels();

println("SO");
for (int g = 30; g <= height - 30; g++) {
println("G " + g);
  // upper
  if (g < my) {
    for (int i = g; i < my; i++) {
      float  rip = random(0, 1);
      float xOffset = random(-10, 10);
      float yOffset = random(-10, 10);

      axeY = i + yOffset;
      axeX = xOffset;

      // upper right
      for (int x = 0; x < width; x++) {
        float n = norm(x, 0.0, float(width));
        float y = pow(n, 2 * rip);
        y *= width;
       
        int o = int(x + (width / 2) + axeX + width * (- y + axeY));
        if (o >= 0 && o < pixels.length) pixels[o] = 255;
        o = int(-x + (width / 2) + axeX + width * (- y + axeY));
        if (o >= 0 && o < pixels.length) pixels[o] = 255;
//        point(x + (width / 2) + axeX, - y + axeY);
//        point(- x + (width / 2) + axeX, - y + axeY);
      }
    }
  }
//  println("I");

  for (int i = g; i < height - 30; i++) {
    float  rip = random(0, 1);
    float xOffset = random(-10, 10);
    float yOffset = random(-10, 10);

    axeY = i + yOffset;
    axeX = xOffset;

    // lower right
    for (int x = 0; x < width; x++) {
      float n = norm(x, 0.0, float(width));
      float y = pow(n, 0.4 * rip);
      y *= width;
      int o = int(x + (width / 2) + axeX + width * (- y + axeY));
      if (o >= 0 && o < pixels.length) pixels[o] = 255;
      o = int(-x + (width / 2) + axeX + width * (- y + axeY));
      if (o >= 0 && o < pixels.length) pixels[o] = 255;
//      point(x + (width / 2) + axeX, y + axeY);
//      point(- x + (width / 2) + axeX, y + axeY);
    }
  }
}

But the output is all black, so either I made an error, or your computations are wrong.

my calculations was correct. in a first part i drew only the upper part and it worked.

Running here, your program didn't seem to complete even 1 iteration of outermost for block g!  

can't understand why your sketch doesn't work on my machine.

P2D is a unique graphics engine @ Processing 1.5.1 and before.

In this newer version, I've used the pixels[] proposed technique from  PhiLho!