Sage Interactions - Fractal

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Mandelbrot's Fractal Binomial Distribution

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])?)

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

Now in 3D

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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 & 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

Julia

by Harald Schilly

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

Sierpiński Triangle

by Eviatar Bach