Iterate over 2d array in an expanding circular spiral

Question

Given an n by n matrix M, at row i and column j, I\'d like to iterate over all the neighboring values in a c

Answer 1

Since it was mentioned that the order of the points do not matter, I've simply ordered them by the angle (arctan2) in which they appear at a given radius. Change N to get more points.

from numpy import *
N = 8

# Find the unique distances
X,Y = meshgrid(arange(N),arange(N))
G = sqrt(X**2+Y**2)
U = unique(G)

# Identify these coordinates
blocks = [[pair for pair in zip(*where(G==idx))] for idx in U if idx<N/2]

# Permute along the different orthogonal directions
directions = array([[1,1],[-1,1],[1,-1],[-1,-1]])

all_R = []
for b in blocks:
    R = set()
    for item in b:
        for x in item*directions:
            R.add(tuple(x))

    R = array(list(R))

    # Sort by angle
    T = array([arctan2(*x) for x in R])
    R = R[argsort(T)]
    all_R.append(R)

# Display the output
from pylab import *
colors = ['r','k','b','y','g']*10
for c,R in zip(colors,all_R):
    X,Y = map(list,zip(*R))

    # Connect last point
    X = X + [X[0],]
    Y = Y + [Y[0],]
    scatter(X,Y,c=c,s=150)
    plot(X,Y,color=c)

axis('equal')
show()

Gives for N=8:

More points N=16 (sorry for the colorblind):

This clearly approaches a circle and hits every grid point in order of increasing radius.