# Sage Interactions - Fractal

## 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])?)

## 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

### 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

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