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Creates an Ulam Spiral as a square matrix of size N.
#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
def create_number_spiral(N):
'''Creates a number spiral as
a square matrix of size N'''
X = np.ndarray((N,N))
ctr = 1
num = 1
if (N%2 == 0):
coord = np.array([(N)/2, (N)/2 - 1], dtype=np.int64)
else:
coord = np.array([(N)/2, (N)/2], dtype=np.int64)
vec = np.array([0,1])
T = np.array([[0, -1], [1, 0]])
while ctr < N:
#Do logic here
k = ctr
while k > 0:
X[coord[0]][coord[1]] = num
#print "Index: ",coord
#print "Vector: ", vec
coord += vec
num += 1
k -= 1
vec = np.dot(T, vec)
k = ctr
while k > 0:
X[coord[0]][coord[1]] = num
#print "Index: ",coord
#print "Vector: ", vec
coord += vec
num += 1
k -= 1
vec = np.dot(T, vec)
#print "Counter: ", ctr
ctr += 1
for ctr in xrange(N):
X[coord[0]][coord[1]] = num
coord += vec
num += 1
return X
def get_primes(n):
'''Returns a list of all primes below n'''
sieve = [True] * n
for i in xrange(3,int(n**0.5)+1,2):
if sieve[i]:
sieve[i*i::2*i]=[False]*((n-i*i-1)/(2*i)+1)
return [2] + [i for i in xrange(3,n,2) if sieve[i]]
def filter_primes(matrix):
'''Takes a matrix and converts it to
a binary array where all primes become
1 and all non primes become 0'''
R = matrix.shape[0]
C = matrix.shape[1]
m = np.zeros((R,C))
prime_list = get_primes(R**2 + 1)
for i in xrange(R):
for j in xrange(C):
if matrix[i][j] in prime_list:
m[i][j] = 128
return m
def prime_spiral_gen(N):
'''Creates a number spiral matrix and
makes all prime numbers 1 and all the
composite numbers 1'''
X = create_number_spiral(200)
Y = filter_primes(X)
plt.imshow(Y, cmap="hot")
plt.show()
prime_spiral_gen(200)
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