Satya Meka ported the open source AEFlame plug-in to After Effects Creative Suite. Recursive Fractal Flames have an interesting history which is discussed in the video embedded here, The Open Source Culture of the Flame Algorithm. Background on flame development in After Effects can be found in the older port to the AE SDK, AEFlame by Andrew Davidson.

AE Flame is a free download from AE Scripts. This version is apparently compatible to AE versions CS3-CS6, so there may be unforeseen problems in AE CC. There's also a tutorial from an earlier version by Victoria Nece, Fanning the AEFlames, and this render from Emilio Madrid:

If you like AE Flame you'll probably like another free filter ported to CS5, Sinedots II by Philipp Spöth (aka Frischluft).  There's a tutorial for that one at AEtuts+, Generate a Dynamic Morphing Background Design with Sinedots by Stefan Surmabojov. Here's a preview:

Somewhat similar designs might also be found in roundups Light Strokes and Streaks and Spirographs in After Effects.

More interesting for this topic is Chaotica, a newer “next-generation fractal art application, designed for both novices and professional artists,” from a group long involved in Flame open-source projects.