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Comment:
← Revision 41 as of 2019-04-06 16:11:28 → ⇥
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Editor: chapoton
Comment: py3 print
Deletions are marked like this. Additions are marked like this.
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html("<h1>Mandelbrot's Fractal Binomial Measure</h1>") pretty_print(html("<h1>Mandelbrot's Fractal Binomial Measure</h1>"))
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def f(A = matrix([[1,1],[-1,1]]), D = '[[0,0],[1,0]]', k=(3..17)):
    print "Det = ", A.det()		 def f(A = matrix([[1,1],[-1,1]]), D = '[[0,0],[1,0]]', k=[3..17]):
    print("Det = {}".format(A.det()))
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def f(A = matrix([[1,1],[-1,1]]), D = '[[0,0],[1,0]]', k=(3..17)):
    print "Det = ", A.det()		 def f(A = matrix([[1,1],[-1,1]]), D = '[[0,0],[1,0]]', k=[3..17]):
    print("Det = {}".format(A.det()))
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def f(A = matrix([[0,0,2],[1,0,1],[0,1,-1]]), D = '[[0,0,0],[1,0,0]]', k=(3..15), labels=True):
    print "Det = ", A.det()		 def f(A = matrix([[0,0,2],[1,0,1],[0,1,-1]]), D = '[[0,0,0],[1,0,0]]', k=[3..15], labels=False):
    print("Det = {}".format(A.det()))
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    print "D:"
    print D		     print("D:")
    print(D)
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    time m=mandelbrot_cython(x0 ,x0 + side ,y0 ,y0 + side , N, L )     m=mandelbrot_cython(x0 ,x0 + side ,y0 ,y0 + side , N, L )
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    time pylab.savefig('mandelbrot.png')     pylab.savefig('mandelbrot.png')
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published notebook: [[http://sagenb.org/pub/1299/]] published notebook: [[https://cloud.sagemath.com/projects/19575ea0-317e-402b-be57-368d04c113db/files/pub/1201-1301/1299-Mandelbrot.sagews]]
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    print 'z <- z^%s + c' % expo     print('z <- z^%s + c' % expo)
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    print 'z <- z^%s + (%s+%s*I)' % (expo, c_real, c_imag)     print('z <- z^%s + (%s+%s*I)' % (expo, c_real, c_imag))

Sage Interactions - Fractal

goto interact main page

Contents

  1. Sage Interactions - Fractal
    1. Mandelbrot's Fractal Binomial Distribution
    2. Fractals Generated By Digit Sets and Dilation Matrices
    3. Demonstrating that the Twin Dragon Matrix is likely to yield a Tiling of a Compact Interval of R^2 as k->infinity (It does!)
    4. Now in 3D
    5. Exploring Mandelbrot
    6. Mandelbrot & Julia Interact with variable exponent
      1. Mandelbrot
      2. Julia
    7. Sierpiński Triangle

Mandelbrot's Fractal Binomial Distribution

binomial.png

Fractals Generated By Digit Sets and Dilation Matrices

(Sage Days 9 - Avra Laarakker)

Attempt at Generating all integer vectors with Digits D and Matrix A (How about vector([0,-1])?)

1.png

Demonstrating that the Twin Dragon Matrix is likely to yield a Tiling of a Compact Interval of R^2 as k->infinity (It does!)

2.png

Now in 3D

3.png

4.png

CategoryCategory

Exploring Mandelbrot

Pablo Angulo 

%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

import pylab
x0_default = -2
y0_default = -1.5
side_default = 3.0
side = side_default
x0 = x0_default
y0 = y0_default
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 )
#    p = (matrix_plot(m) +
#             line2d([(N/2,0),(N/2,N)], color='red', zorder=2) +
#             line2d([(0,N/2),(N,N/2)], color='red', zorder=2))
#    time show(p, figsize = (plot_size, plot_size))
    pylab.clf()
    pylab.imshow(m, cmap = pylab.cm.gray)
    pylab.savefig('mandelbrot.png')

mandelbrot_cython.png

Mandelbrot & Julia Interact with variable exponent

published notebook: https://cloud.sagemath.com/projects/19575ea0-317e-402b-be57-368d04c113db/files/pub/1201-1301/1299-Mandelbrot.sagews

Mandelbrot

by Harald Schilly

mandel-interact-02.png

Julia

by Harald Schilly

julia-interact-01.png 

julia_plot(-7,30,0.5,0.5,(-1.5,1.5), (-1.5,1.5))

julia-fractal-exponent--7.png

Sierpiński Triangle

by Eviatar Bach

sierpinski.png

interact/fractal (last edited 2019-04-06 16:11:28 by chapoton)