Julia set code creates a circle instead of a fractal

Question

I have this code:

from PIL import Image
import colorsys

xmin, xmax = -2.0, 2.0
ymin, ymax = -2.0, 2.0

depth = 12

imgx, imgy = 512, 512

maxIter = 256

image = Image.new("RGB", (imgx, imgy))

for y in range(imgy):
    cy = y * (ymax - ymin)/(imgy - 1) + ymin
    for x in range(imgx):
        cx = x * (xmax - xmin)/(imgx - 1) + xmin
        c = complex(cx, cy)
        z = 0
        for i in range(maxIter):
            if abs(z) > 2.0:
                break
            z = c + complex(0.25, 0.1)
        r = i
        g = int((i*50)%256)
        b = int(255 - i)
        image.putpixel((x, y), (r, g, b))

It creates an image of a circle (image below), and I can't understand why. I think it might have something to do with the for loops and the if statements, but I can't figure out what the problem would be. If it's not that, what is it?

Side note: this code is adapted from a Mandelbrot set code I wrote. The only difference is that instead of z = c + complex(0.25, 0.1), I have z = z**2 + c.

Julia Set

Answer 1

This line:

z = c + complex(0.25, 0.1)

always yields the same value (current point + a constant) in each iteration, so your code just draws a circle. Change that line to

z = z**2 + complex(0.25, 0.1)

and initialize z based on the current point (like c is in your current code).