An interactive graph to plot the trajectory of points on and off the mandelbrot set. Illustrates the use of sliders in matplotlib
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 | """An interactive graph to plot the trajectory of points on and off the mandelbrot
set. Illustrates the use of sliders in matplotlib"""
import pylab
from matplotlib.widgets import Slider
def compute_trajectory(x0, y0, set_boundary = 2, n_iters = 100):
"""Take the fragment and compute a further n_iters iterations for each element
that has not exceeded the bound. Also indicate if we are inside or outside the
mandelbrot set"""
set = True
C = complex(x0, y0)
Z = pylab.ones(n_iters,'complex')*C
for n in range(n_iters-1):
if abs(Z[n]) > set_boundary:
Z[n+1:] = Z[n]
set = False
break
Z[n+1] = Z[n]*Z[n] + C
return Z, set
axcolor = 'lightgoldenrodyellow'
ax_x = pylab.axes([0.1, 0.04, 0.8, 0.03], axisbg=axcolor)
ax_y = pylab.axes([0.1, 0.01, 0.8, 0.03], axisbg=axcolor)
sx = Slider(ax_x, 'x', -1.0, 1.0, valinit=0)
sy = Slider(ax_y, 'y', -1.0, 1.0, valinit=0)
ax_plot = pylab.axes([0.12, 0.12, 0.85, 0.85])
Z,s = compute_trajectory(0,0)
l, = pylab.plot(Z.real, Z.imag,'.-') #Ain't that cool?
st, = pylab.plot(Z[0].real, Z[0].imag,'ok')
pylab.setp(ax_plot,'xlim',[-1,1], 'ylim', [-1,1])
#pylab.axis('scaled')
m_set = [[0],[0]]
ms, = pylab.plot(m_set[0], m_set[1],'k.')
def update(val):
x = sx.val
y = sy.val
Z, set = compute_trajectory(x,y)
l.set_xdata(Z.real)
l.set_ydata(Z.imag)
st.set_xdata(Z[0].real)
st.set_ydata(Z[0].imag)
if set:
m_set[0] += [x]
m_set[1] += [y]
ms.set_xdata(m_set[0])
ms.set_ydata(m_set[1])
pylab.draw()
sx.on_changed(update)
sy.on_changed(update)
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