Mathematica Cookbook

Chapter 15. Interactivity

I’m alive Oh oh, so alive I’m alive Oh oh, so alive ... My head is full of magic, baby And I can share this with you The feel I’m on top again, baby That’s got everything to do with you

—Love and Rockets, “So Alive”

15.0 Introduction

The pièce de résistance of Mathematica 6 is its dynamic interactivity features. These features forced Wolfram to completely rethink and redesign its frontend. This had the unfortunate consequence of breaking many notebooks from version 5 and earlier, especially those that used graphics. However, it is my opinion that the gain was well worth the pain!

The interactive features of Mathematica 6 are even more impressive when one considers that they sit on relatively few new functions. The centerpiece of interactivity is the function Manipulate. Think of Manipulate as a very intelligent user-interface generator. Manipulate’s power comes by virtue of its ability to take any Mathematica expression plus a declarative description of the expression’s variables and generate a mini embedded GUI within the notebook for interacting with that expression. Of course, there are always caveats, and an important feature of this chapter is to help you get the best possible results with nontrivial Manipulate use cases.

The first five recipes of this chapter are intended to gradually introduce the reader to Manipulate by demonstrating increasingly sophisticated examples. These recipes are not necessarily intended for direct use but rather to illustrate ...