I have used 2 for loops to check if the points are within the set, but apparently it takes too much time, giving less details on the plot itself. How can I optimise the code to run faster, and thus add more detail to the plot ? The pygame origin is at the top left corner, so I manually set each point relative to the centre.
import math
import pygame
class Point:
def __init__(self, x, y):
self.x = x - 250
self.y = y - 250
class Complex:
def __init__(self, real, imaginary):
self.real = real
self.imaginary = imaginary
def __eq__(self, other):
if self.real == other.real:
if self.imaginary == other.imaginary:
return True
return False
def __abs__(self):
return math.sqrt(self.real ** 2 + self.imaginary ** 2)
def __round__(self, n=None):
return Complex(round(self.real, 4), round(self.imaginary, 4))
def __add__(self, other):
return Complex(self.real + other.real, self.imaginary + other.imaginary)
def __sub__(self, other):
return Complex(self.real - other.real, self.imaginary - other.imaginary)
def __mul__(self, other):
return Complex((self.real * other.real) - (self.imaginary * other.imaginary),
(self.real * other.imaginary) + (self.imaginary * other.real))
def zheta(z, c):
return round((z * z) + c, 3)
def mandelbrotNumber(num):
z0 = Complex(0, 0)
c = num
checkList = [Complex(0, 0)]
for i in range(10):
z = zheta(z0, c)
if abs(z) > 2:
return False
if z in checkList:
return True
checkList.append(z)
z0 = z
return True
def plotPoint(x, y):
color = (0, 0, 0)
position = (x, y)
pygame.draw.circle(screen, color, position, 2)
pygame.init()
screen = pygame.display.set_mode((500, 500))
running = True
startPosX = (0, 250)
endPosX = (500, 250)
startPosY = (250, 0)
endPosY = (250, 500)
while running:
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
screen.fill("white")
for i in range(-200, 200):
for j in range(-200, 200):
number = Complex(i / 100, j / 100)
if mandelbrotNumber(number):
plotPoint((number.real*100) + 300, (number.imaginary*100) + 250)
pygame.display.flip()
pygame.quit()
for i in range(10):you seem only to iterate to a very shallow depth. That will give a rudimentary Mandelbrot set. Not my DV.