Randomness of Python's random

I'm using Python to generate images using dashed lines for stippling. The period of the dashing is constant, what changes is dash/space ratio.

This produces something like this:

However in that image the dashing has a uniform origin and this creates unsightly vertical gutters. So I tried to randomize the origin to remove the gutters. This sort of works but there is an obvious pattern:

Wondering where this comes from I made a very simple test case with stacked dashed straight lines:

  • dash ratio: 50%
  • dash period 20px
  • origin shift from -10px to +10px using random.uniform(-10.,+10.)(*) (after an initial random.seed()

And with added randomness:

So there is still pattern. What I don't understand is that to get a visible gutter you need to have 6 or 7 consecutive values falling in the same range (says, half the total range), which should be a 1/64 probability but seems to happen a lot more often in the 200 lines generated.

Am I misunderstanding something? Is it just our human brain which is seeing patterns where there is none? Could there be a better way to generate something more "visually random" (python 2.7, and preferably without installing anything)?

(*) partial pixels are valid in that context

Annex: the code I use (this is a Gimp script):

#!/usr/bin/env python
# -*- coding: iso-8859-15 -*-
Python script for Gimp (requires Gimp 2.10)
Run on a 400x400 image to see something without having to wait too much
Menu entry is in "Test" submenu of image menubar

import random,traceback
from gimpfu import *

def constant(minShift,maxShift):
return 0

def triangle(minShift,maxShift):
return random.triangular(minShift,maxShift)

def uniform(minShift,maxShift):
return random.uniform(minShift,maxShift)

def gauss(minShift,maxShift):
return random.gauss((minShift+maxShift)/2,(maxShift-minShift)/2)


def generate(image,name,generator):
layer=gimp.Layer(image, name, image.width, image.height, RGB_IMAGE,100, LAYER_MODE_NORMAL)

# Generate path, horizontal lines are 2px apart, 
# Start on left has a random offset, end is on the right edge right edge
for i in range(1,image.height, 2):

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