Mandelbrot Set Problem 2 Part b (6 points). Visualize the Mandelbrot set M using the following steps: 1. Make an mm grid of evenly spaced points in the square region R=[2,1][1.5,1.5] with m=103. Generate the points using the linspace method and create a grid using meshgrid. It can be shown that the Mandelbrot set M belongs to R. 2. For each grid point c=x+iy : calculate the orbit fc(0)={z0=0,zn=zn12+c} for n=1,2,,N=500 and record the corresponding smallest kN for which zk>2. If zk2 for all k=0,1,,N, then set k=N+1=501. If kN, then we say that c/A; if k=N+1, then cA. 3. Visualize the Mandelbrot set as described below. Some setup and structure are provided % set m and N m=103;% grid size N=50;% number of iterations % set x and y domain x_bounds =[2,1];% limits in the x-direction ybounds=[1.5,1.5];% limits in the y-direction \% Make m linearly spaced points in x and y across bounds x= linspace(x_bounds (1),xbounds (2),m);% x-coordinates of grid points y= linspace( "fill in"); %-coordinates of grid points \% Combine x and y into a grid using meshgrid [ "collect output here " ]= meshgrid (x,y); \% Calculate c from the x grid and y grid \% Multiplying by vector 1i instead of scalar i is faster and more robust c= "x output" +1i "y output"; \% Create a counter: counts how many iterations are needed to escape from {z:z