When it comes to differential equations, many online graphing calculators can easily generate slope fields and graph out a few possible solutions for you.
I, however, am interested in functional equations, and functional iteration in particular. Does anybody know of any online software that manually graphs iterations of functions for you (particularly fractional iterations)? This would be very helpful to me.
If nobody knows of this type of software, can anybody recommend any manual graphing techniques (analogous to graphing a slope field by hand for a differential equation)? As an example, could somebody provide a graph of the functional square root of $e^x$?
I know it can be done, because on Wikipedia, it shows a number of graphs of the fractional and negative iterates of the sine function:
Thanks!
