Dilshod Davronov - 4 months ago 43

Python Question

this is the task I get:

Complex numbers can be represented on a two-dimensional space. Consider complex numbers cc of the form c=x+1j*y (j is the imaginary unit), where x∈[−2,0.5] and y∈[−1,1]. Imagine to have a two-dimensional grid in this space, with each step of the grid being 10ˆ(-2) . For each c corresponding to one of the nodes of the grid, calculate the iterative function

`Z_{n+1} = Zˆ2_n + c`

Since I am not a math student, I am in trouble with that. So far, I could do till this point:

`import numpy as np`

x_values = np.arange(-2, 0.5, 0.01)

y_values = np.arange(-1, 1, 0.01)

M = np.zeros((len(x_values), (len(y_values))), dtype = "complex")

for x in range(len(x_values)):

for y in range(len(y_values)):

M[x][y] = x_values[x] +1j*y_values[y]

could you tell me how I can define a function that takes a grid/array like the one we have, initializes z=0 and then 100 times (i.e. for n in range(100)) does: z = z**2 + grid

then after the loop return z.

then to plot the image:

Answer

You were almost there!

Just add a little bit more to your `for`

-loops:

```
for x in range(len(x_values)):
for y in range(len(y_values)):
for i in range(100):
M[x][y] = M[x][y]**2 + (x_values[x] + 1j*y_values[y])
```

(I don't have numpy available at the moment, so I couldn't test it, but it's not too complicated so it's probably fine.)

As for the plotting, I suggest checking out matplotlib. If you have trouble, ask another SO question. But until you've tried something, I don't want to just write the whole thing for you. ;)