unfinished example of how to render to a tkinter PhotoImage, pixel by pixel

mandelbrot.py

import tkinter as tk

WIDTH, HEIGHT = 512, 512
TOP, LEFT = 1.5, -2.0
BOTTOM, RIGHT = -1.5, 1.0
STEPS = 256


def mandelbrot(x, y):
    a = b = 0
    for i in range(STEPS):
        a, b = a**2 - b**2 + x, 2 * a * b + y
        if a**2 + b**2 >= 4:
            break
    return (i + 1) % STEPS


class App(tk.Tk):
    x = 0
    y = 0

    def __init__(self):
        super().__init__()
        self.title = 'Live Update PhotoImage Demo'

        self.img = tk.PhotoImage(width=WIDTH, height=HEIGHT)
        self.after(10, self.render)

        self.canvas = tk.Canvas(self, width=WIDTH, height=HEIGHT, bg="blue")
        self.canvas.create_image(WIDTH, HEIGHT, image=self.img, anchor=tk.SE)
        self.canvas.pack()

    def render(self):
        v = mandelbrot(
            LEFT + (RIGHT - LEFT) / WIDTH * self.x,
            TOP + (BOTTOM - TOP) / HEIGHT * self.y
        )
        v = pow(v, 3) % 256
        self.img.put(f'#{v:02x}{v:02x}{v:02x}', (self.x, self.y))

        self.x = (self.x + 1) % WIDTH
        if self.x == 0:
            self.y = (self.y + 1) % HEIGHT

        if not self.x == self.y == 0:
            self.after(1, self.render)


if __name__ == "__main__":
    app = App()
    app.mainloop()