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def qmul(A_x, A_y, A_z, A_w, B_x, B_y, B_z, B_w): | |
C_x = A_x*B_x - A_y*B_y - A_z*B_z - A_w*B_w | |
C_y = A_x*B_y + A_y*B_x + A_z*B_w - A_w*B_z | |
C_z = A_x*B_z - A_y*B_w + A_z*B_x + A_w*B_y | |
C_w = A_x*B_w + A_y*B_z - A_z*B_y + A_w*B_x | |
return C_x, C_y, C_z, C_w | |
def qadd(A_x, A_y, A_z, A_w, B_x, B_y, B_z, B_w): | |
C_x = A_x + B_x | |
C_y = A_y + B_y | |
C_z = A_z + B_z | |
C_w = A_w + B_w | |
return C_x, C_y, C_z, C_w | |
# Quaternion Julia set Z = Z*Z + C | |
def quat_function(x, y, z): | |
Z_x = x | |
Z_y = y | |
Z_z = z | |
Z_w = 0 | |
C_x = 0.3 # values of 0 for C make for a unit ball | |
C_y = 0.5 | |
C_z = 0.4 | |
C_w = 0.2 | |
threshold = 4 | |
max_iterations = 8 | |
len_sq = Z_x*Z_x + Z_y*Z_y + Z_z*Z_z + Z_w*Z_w | |
threshold_sq = threshold*threshold | |
for i in range(0, max_iterations): | |
Z_x, Z_y, Z_z, Z_w = qmul(Z_x, Z_y, Z_z, Z_w, Z_x, Z_y, Z_z, Z_w) # Z*Z | |
Z_x, Z_y, Z_z, Z_w = qadd(Z_x, Z_y, Z_z, Z_w, C_x, C_y, C_z, C_w) # + C | |
len_sq = Z_x*Z_x + Z_y*Z_y + Z_z*Z_z + Z_w*Z_w | |
if len_sq > threshold_sq: | |
break; | |
return threshold - math.sqrt(len_sq) |
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