Differences between revisions 19 and 27 (spanning 8 versions)
⇤ ← Revision 19 as of 2010-10-29 20:08:52 →
Size: 7375
Editor: pang
Comment: modified "exploring mandelbrot": faster and more intuitive
← Revision 27 as of 2012-04-18 18:02:48 → ⇥
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Editor: bvarberg
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Deletions are marked like this. Additions are marked like this.
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{{{ {{{#!sagecell
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{{{ {{{#!sagecell
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{{{ {{{#!sagecell
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== Now in 3d ==
    
{{{		 == Now in 3D ==
    
{{{#!sagecell
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{{{ {{{#!sagecell
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    cdef np.ndarray[int, ndim=2] m
    m = np.zeros((N,N), dtype=int)		     cdef np.ndarray[np.uint16_t, ndim=2] m
    m = np.zeros((N,N), dtype=np.uint16)
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{{{ {{{#!sagecell
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    print option
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    elif option == 'Stay':
        pass
    else:		     elif option != 'Stay':
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    time pylab.savefig('caca.png')     time pylab.savefig('mandelbrot.png')
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{{{ {{{#!sagecell
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      formula = list(['mandel','ff']),\       formula = ['mandel','ff'],\
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{{{ {{{#!sagecell
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== Sierpiński Triangle ==
by Eviatar Bach

{{{#!sagecell
%python

from numpy import zeros

def sierpinski(N):
    '''Generates the Sierpiński Triangle fractal to N iterations using the Rule 90 elementary cellular automaton. N is in powers of 2 because these produce "whole" triangles.'''
    M=zeros( (N,2*N+1), dtype=int)
    M[0,N]=1
    rule=[0, 1, 0, 1, 1, 0, 1, 0]
    
    for j in range(1,N):
        for k in range(N-j,N+j+1):
            l = 4*M[j-1,k-1] + 2*M[j-1,k] + M[j-1,k+1]
            M[j,k]=rule[ l ]
    return M
    
@interact
def _(N=slider([2**a for a in range(0, 12)], label='Number of iterations',default=128), size = slider(1, 20, label= 'Size', step_size=1, default=9 )):
    M = sierpinski(N)
    plot_M = matrix_plot(M, cmap='binary')
    plot_M.show( figsize=[size,size])
}}}
{{attachment:sierpinski.png}}

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 (Sage Days 9 - Avra Laarakker)
    3. Attempt at Generating all integer vectors with Digits D and Matrix A (How about vector([0,-1])?)
    4. Demonstrating that the Twin Dragon Matrix is likely to yield a Tiling of a Compact Interval of R^2 as k->infinity (It does!)
    5. Now in 3D
    6. Exploring Mandelbrot
    7. Mandelbrot & Julia Interact with variable exponent
      1. Mandelbrot
      2. Julia
    8. 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

mandelbrot_cython.png

Mandelbrot & Julia Interact with variable exponent

published notebook: http://sagenb.org/pub/1299/

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)