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An interactive graph to plot the trajectory of points on and off the mandelbrot set. Illustrates the use of sliders in matplotlib

Python, 56 lines
 ``` 1 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) ```
 Created by Kaushik Ghose on Wed, 6 Apr 2011 (MIT)