## Monday, August 22, 2011

### 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)
l1, = plot(None,None, lw=2, color='red')
axis([-1, 1, -8, 8])
title ('\$(a + bi)t\$', color='blue')
grid()

ax = subplot(122)
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()
```