Plotting a Complex Exponential

We rewrote one of the MIT OCW 18.03 ODE Mathlets in Python. This mathlet was for plotting complex exponentials.

from pylab import *

from matplotlib.widgets import Slider



ax = subplot(121)

subplots_adjust(left=0.1, bottom=0.25)

l1, = plot(None,None, lw=2, color='red')

axis([-1, 1, -8, 8])

title ('$(a + bi)t$', color='blue')

grid()



ax = subplot(122)

subplots_adjust(left=0.1, bottom=0.25)

l2, = plot(None,None, lw=2, color='red')

axis([-3, 3, -3, 3])

title ('$e^{(a + bi)t}$', color='blue')

grid()



axcolor = 'lightgoldenrodyellow'

axa = axes([0.15, 0.1, 0.65, 0.03], axisbg=axcolor)

axb  = axes([0.15, 0.15, 0.65, 0.03], axisbg=axcolor)



slidera = Slider(axa, 'a', -1.0, 1.0, valinit=0)

sliderb = Slider(axb, 'b', -8.0, 8.0, valinit=0)



def update(val):

    a = slidera.val

    b = sliderb.val

    t = arange(-1.0, 1.0, 0.001)

    l1.set_xdata(t)

    l1.set_ydata((b/a)*t)



    t = arange(-3.0, 3.0, 0.001)

    l2.set_xdata(exp(a*t)*cos(b*t))

    l2.set_ydata(exp(a*t)*sin(b*t))

    draw()



slidera.on_changed(update)

sliderb.on_changed(update)



show()