What exactly is a gnarl? Well, let's try Wiktionary for starters...
- (mathematics) The average value of the magnitude squared of the curl of a vector field over a continuous path that is tangent to the vector field at every point. In mathematical notation, gnarl is represented by the lowercase Greek letter ξ
Okay. Unless you're a math geek that's not very helpful...
How about what a gnarl isn't? A gnarl is not a fractal (despite the fact that fractal software programs support the creation of them). While gnarls exhibit some self-similarity, they do not have infinite resolution, nor are they recursive. In other words, unlike a fractal, you can't keep zooming in on a gnarl and find more details or other gnarls.
However, like fractals, gnarls are to be found everywhere in nature. From knots on trees, to weather patterns and clouds, to the smoke that rises from a cigarette or some incense, to an ink drop in a glass of water. Basically wherever fluidic movements are to be found, you'll see gnarls. In practice, though, gnarls can range from curvy shapes, to intricate patterns, to geometric forms, and into wonderfully abstract shapes. In short, gnarls are very cool, and that's why we make them.
All major fractal programs support the creation of gnarls (Apophysis, Chaotica, UltraFractal, and mandelbulb3D). I have to admit that I don't understand how they work in flame-based fractal programs (that stuff is all high weirdness/sorcery to me), so I'll mainly focus on how they are created in UltraFractal. But for completeness sake, here are some gnarls created in Apophysis and Chaotica:
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UltraFractal works a bit differently, being formula-based. If you search for 'gnarl' in the public formulas, you'll find a number of them that will work. Also, anything called "Dynamic", "Popcorn", "Vine", "Martin" or "Glyph" will also give you gnarly forms. There are also a number of coloring algorithms that feature these formulas. So explore! And when you get tired of those, and want a real challenge, download ReFa1's Very Advanced Gnarl formula:
And don't forget JayceCruel's gnarl formula:
Both formulas are beasts in their own right, and should provide you with limitless possibilities to explore and create. 
Here are some examples of UltraFractal gnarls:
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If you want to check out more gnarls, visit 
There are also tutorials there to get you started. Have fun.
There are also tutorials there to get you started. Have fun. -sk
I love gnarls. ;)