CoCalc Public Filessupport / 2018-02-02-mandelbrot.sagews
Author: William A. Stein
Description: Jupyter notebook support/2015-06-04-141749-bokeh.ipynb

Mandelbrot set. From https://wiki.sagemath.org/interact/fractal

%auto %cython import numpy as np cimport numpy as np def mandelbrot_cython(float x0,float x1,float y0,float y1, int N=200, int L=50, float R=3): '''returns an array NxN to be plotted with matrix_plot ''' cdef double complex c, z, I cdef float deltax, deltay, R2 = R*R cdef int h, j, k cdef np.ndarray[np.uint16_t, ndim=2] m m = np.zeros((N,N), dtype=np.uint16) I = complex(0,1) deltax = (x1-x0)/N deltay = (y1-y0)/N for j in range(N): for k in range(N): c = (x0+j*deltax)+ I*(y0+k*deltay) z=0 h=0 while (h<L and z.real**2 + z.imag**2 < R2): z=z*z+c h+=1 m[j,k]=h return m
Defined mandelbrot_cython, np
Auto-generated code...
%auto import pylab x0_default = -2 y0_default = -1.5 side_default = 3.0 side = side_default x0 = x0_default y0 = y0_default N = 100 L = 20
%time m=mandelbrot_cython(x0 ,x0 + side ,y0 ,y0 + side , N, L ) pylab.clf() pylab.imshow(m, cmap = pylab.cm.gray)
CPU time: 0.06 s, Wall time: 0.07 s
options = ['Reset','Upper Left', 'Upper Right', 'Stay', 'Lower Left', 'Lower Right'] @interact def show_mandelbrot(option = selector(options, nrows = 2, width=8), N = slider(100, 1000,100, 300), L = slider(20, 300, 20, 60), plot_size = slider(2,10,1,6), auto_update = False): global x0, y0, side if option == 'Lower Right': x0 += side/2 y0 += side/2 elif option == 'Upper Right': y0 += side/2 elif option == 'Lower Left': x0 += side/2 if option=='Reset': side = side_default x0 = x0_default y0 = y0_default elif option != 'Stay': side = side/2 m=mandelbrot_cython(x0 ,x0 + side ,y0 ,y0 + side , N, L ) pylab.clf() pylab.imshow(m, cmap = pylab.cm.gray) pylab.show()