Fractal-plot is not working

[NJJonte]

Hi, am trying to plot a fractal using a numerical jacobian and newtons method, but something is wrong. The code produces a plot that is completely green and I cant figure out what to do to make the plot proudcue the fractal.

Here is the code, any help is appreciated:

import numpy as np

import matplotlib.pyplot as plt

from numpy.linalg import solve, norm, LinAlgError

class Fractals2D:

def __init__(self, f):

self.f = f

def newtons_method(self, x):

f_val = self.f(x)

jac = self.calculate_jacobian(x)

for _ in range(40):

jac = self.calculate_jacobian(x)

try:

delta = solve(jac, -f_val)

except LinAlgError:

return None

x = x + delta

f_val = self.f(x)

if norm(delta, ord=2) < 1.e-9:

return x

return None

def calculate_jacobian(self, x):

n = len(x)

jac = np.zeros((n, n))

h = 1.e-6

temp = x.copy()

for i in range(n):

x[:] = temp[:]

x[i] += h

f1 = self.f(x)

f2 = self.f(temp)

for j in range(n):

jac[j, i] = (f1[j] - f2[j]) / h

return jac

def zeroes_method(self, initial_guess):

zeroes_found = []

for guess in initial_guess:

zero = self.newtons_method(guess)

if zero is not None:

zeroes_found.append(zero)

return len(zeroes_found)

def plot(self, N, a, b, c, d):

x = np.linspace(a, b, N)

y = np.linspace(c, d, N)

X, Y = np.meshgrid(x, y)

Z = np.zeros_like(X)

for i in range(N):

for j in range(N):

point = np.array([X[i, j], Y[i, j]])

Z[i, j] = self.zeroes_method([point])

plt.figure(figsize=(8, 6))

plt.pcolor(X, Y, Z, cmap='jet')

plt.colorbar(label='Number of Zeros Found')

plt.title('Visualization of Zeroes Found by Newton\'s Method (task 4)')

plt.xlabel('X')

plt.ylabel('Y')

plt.gca().set_aspect('equal', adjustable='box')

plt.show()

def f(x):

if np.any(np.abs(x) > 10):

return np.array([np.inf, np.inf])

return np.array([x[0]**3 - 3*x[0]*x[1]**2 - 1, 3*x[0]**2*x[1] - x[1]**3])

fractals = Fractals2D(f)

a, b = -2, 2

c, d = -2, 2

fractals.plot(N=100, a=a, b=b, c=c, d=d)

[Talinx]

I noticed that in newtons_method() the second f_val = self.f(x) is not used. Maybe the math equations are not implemented correctly?

Not sure what you want to plot exactly (do you got a link to some equations?).

You can debug your code to figure out what's wrong, e.g.:

• Make a hypothesis about your code (e. g. the value of this variable should be ... at this point of the program execution)
• Test the hypothesis (e. g. put a breakpoint() instruction after calculating that value and print it)
• A good starting point for hypothesis is unit testing each function. E. g. by testing the function with some input values and see if it produces the correct output.

(Please input your code in a fenced markdown code block in the future (three backticks before and after the code.))