[6991] | 1 | """Fundamental routines for computing the Mandelbrot set |
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| 2 | |
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| 3 | Ole Nielsen, SUT 2003 |
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| 4 | """ |
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| 5 | |
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| 6 | def balance(N, P, p): |
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| 7 | """Compute p'th interval when N is distributed over P bins. |
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| 8 | """ |
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| 9 | |
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| 10 | from math import floor |
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| 11 | |
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| 12 | L = int(floor(float(N)/P)) |
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| 13 | K = N - P*L |
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| 14 | if p < K: |
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| 15 | Nlo = p*L + p |
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| 16 | Nhi = Nlo + L + 1 |
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| 17 | else: |
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| 18 | Nlo = p*L + K |
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| 19 | Nhi = Nlo + L |
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| 20 | |
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| 21 | return Nlo, Nhi |
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| 22 | |
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| 23 | |
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| 24 | def calculate_point(c, kmax): |
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| 25 | """Python version for calculating on point of the set |
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| 26 | This is slow and for reference purposes only. |
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| 27 | Use version from mandel_ext instead. |
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| 28 | """ |
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| 29 | |
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| 30 | z = complex(0,0) |
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| 31 | |
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| 32 | count = 0 |
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| 33 | while count < kmax and abs(z) <= 2: |
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| 34 | z = z*z + c |
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| 35 | count += 1 |
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| 36 | |
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| 37 | return count |
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| 38 | |
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| 39 | |
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| 40 | def calculate_region(real_min, real_max, imag_min, imag_max, kmax, M, N, |
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| 41 | Mlo = 0, Mhi = None, Nlo = 0, Nhi = None): |
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| 42 | """Calculate the mandelbrot set in the given region with resolution M by N |
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| 43 | If Mlo, Mhi or Nlo, Nhi are specified computed only given subinterval. |
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| 44 | """ |
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| 45 | |
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| 46 | from numpy import zeros |
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| 47 | from mandel_ext import calculate_point #Fast C implementation |
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| 48 | |
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| 49 | if Mhi is None: Mhi = M |
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| 50 | if Nhi is None: Nhi = N |
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| 51 | |
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| 52 | real_step = (real_max-real_min)/M |
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| 53 | imag_step = (imag_max-imag_min)/N |
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| 54 | |
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| 55 | A = zeros((M, N), dtype='i') # Create M x N matrix |
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| 56 | |
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| 57 | for i in range(Mlo, Mhi): |
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| 58 | for j in range(Nlo, Nhi): |
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| 59 | c = complex(real_min + i*real_step, imag_min + j*imag_step) |
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| 60 | A[i,j] = calculate_point(c, kmax) |
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| 61 | |
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| 62 | return A |
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| 63 | |
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| 64 | |
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| 65 | |
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| 66 | def calculate_region_cyclic(real_min, real_max, imag_min, imag_max, kmax, |
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| 67 | M, N, p=0, P=1, row = 1): |
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| 68 | """Calculate rows p+nP, n in N of the mandelbrot set in the given region |
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| 69 | with resolution M by N |
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| 70 | |
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| 71 | This is the most efficient way of partitioning the work. |
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| 72 | """ |
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| 73 | |
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| 74 | |
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| 75 | from numpy import zeros |
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| 76 | from mandel_ext import calculate_point #Fast C implementation |
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| 77 | |
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| 78 | real_step = (real_max-real_min)/M |
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| 79 | imag_step = (imag_max-imag_min)/N |
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| 80 | |
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| 81 | A = zeros((M, N), dtype='i') # Create M x N matrix |
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| 82 | |
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| 83 | if row: |
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| 84 | for i in range(M): |
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| 85 | if i%P == p: |
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| 86 | for j in range(N): |
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| 87 | c = complex(real_min + i*real_step, imag_min + j*imag_step) |
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| 88 | A[i,j] = calculate_point(c, kmax) |
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| 89 | else: |
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| 90 | for j in range(N): |
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| 91 | if j%P == p: |
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| 92 | for i in range(M): |
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| 93 | c = complex(real_min + i*real_step, imag_min + j*imag_step) |
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| 94 | A[i,j] = calculate_point(c, kmax) |
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| 95 | return A |
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| 96 | |
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| 97 | |
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