# Make a grid for computing a Mandelbrot set with outer product in Python

Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product  is −

[[a0*b0 a0*b1 ... a0*bN ]
[a1*b0 .
[ ... .
[aM*b0    aM*bN ]]

To get the Outer product of two arrays, use the numpy.outer() method in Python. The numpy.ones() return a new array of given shape and type, filled with ones. The numpy.linspace() returns evenly spaced numbers over a specified interval.

## Steps

At first, import the required libraries −

import numpy as np


The real part −

rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
print("The real part of the complex number...\n",rl)

The imaginary part −

im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
print("\nThe imaginary part of the complex numbers...\n",rl)

Forming a grid −

grid = rl + im


## Example

import numpy as np

# To get the Outer product of two arrays, use the numpy.outer() method in Python
# The numpy.ones() return a new array of given shape and type, filled with ones.
# The numpy.linspace() returns evenly spaced numbers over a specified interval.
# The real part
rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
print("The real part of the complex number...\n",rl)

# The imaginary part
im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
print("\nThe imaginary part of the complex numbers...\n",rl)

# Forming a grid
grid = rl + im
print("\nDisplaying the grid...\n",grid)

## Output

The real part of the complex number...
[[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]]

The imaginary part of the complex numbers...
[[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]
[-2. -1. 0. 1. 2.]]

Displaying the grid...
[[-2.+2.j -1.+2.j 0.+2.j 1.+2.j 2.+2.j]
[-2.+1.j -1.+1.j 0.+1.j 1.+1.j 2.+1.j]
[-2.+0.j -1.+0.j 0.+0.j 1.+0.j 2.+0.j]
[-2.-1.j -1.-1.j 0.-1.j 1.-1.j 2.-1.j]
[-2.-2.j -1.-2.j 0.-2.j 1.-2.j 2.-2.j]]