juliaVariableExp.sagews

@interact
def julia_plot(expo = slider(-10,10,0.1,2), \
      iterations=slider(1,100,1,30), \
      c_real = slider(-2,2,0.01,0.5), \
      c_imag = slider(-2,2,0.01,0.5), \
      zoom_x = range_slider(-2,2,0.01,(-1.5,1.5)), \
      zoom_y = range_slider(-2,2,0.01,(-1.5,1.5))):
    var('z')
    I = CDF.gen()
    f(z) = z^expo + c_real + c_imag*I
    ff_j = fast_callable(f, vars=[z], domain=CDF)

    def julia(z):
      for i in range(iterations):
         z = ff_j(z)
         if abs(z) > 2:
            return z
      return z
    print 'z <- z^%s + (%s+%s*I)' % (expo, c_real, c_imag)

    complex_plot(julia, zoom_x,zoom_y, plot_points=200, dpi=150).show(frame=True, aspect_ratio=1)

Interact: please open in CoCalc