List of the most common types of fractals

[Chillheimer]

Hello everyone!
For http://fractalogy.org/ and the "fractal" menu there I'm working on an overview of the most important fractal types.
The current structure is no good.
As I'm more a visual person than a mathematician I definitely need help on this one.
I've tried to use Paul Bourkes great site to start such a list, but I'm stuck, my math background just isn't sufficient.

Soo, could you guys help with a rough classification of fractals? Limited to a max of... 10, preferrably less *categories - that will branch into **sub categories, something like:

* Diffusion Limited..
**Aggregation
**Platonic Solids
...
* Attractors
**Strange Attractor
**Lorenz Attractor
**Henon Attractor
...
* Complex Number fractals
**Mandelbrot-Set
**Burning Ship
**Julia Set
*IFS
**Lindenmayer systems
**Koch Curve
**Cantor Set(?)
...


If you can't make a complete list, please just shout out whatever main category you think is essential, or what sub-branch is missing. Also any other thought regarding a suitable structure is very welcome!

Or maybe you know a good link to a list with good structure

[Madman]

You could try Tglad's system. It differentiates in a different way than you propose, but it might be what you are looking for. It must be somewhere here on the forums...

[Max Sinister]

Menger sponge, Sierpinski triangle / carpet; also, I heard the term Cantor dust.

[DarkBeam]

Attractors? There are lots of them indeed.

A list can be: http://www.bentamari.com/attractors.html

In your list you forgot all escape time classic fractals? Mandelbrot and Julia modes... Nevermind I did not read

[Adam Majewski]

https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

http://incendia.net/wiki/index.php/Fractal_Types
http://www.nahee.com/spanky/www/fractint/fractal_types.html

https://en.wikibooks.org/wiki/Fractals

[rsidwell]

I like to categorize fractals by how they are defined. The most common I've seen are:

* Recursive geometric operations
** L-systems
** iterative deletions (e.g., Cantor set, Sierpinski gasket, Menger sponge)

* Random fractals
** DLA
** fBm

* Orbital fractals
** strange attractors (e.g. Lorentz, Hénon, Rössler)
** IFS
** fractal flames

* Escape-time fractals
** Julia sets
** Mandelbrot sets
** Mandelbulbs

The last two both use orbits of points obtained by repeated iteration of functions. With Orbital fractals, the fractal consists of the orbit points; with Escape-time fractals, the fractal consists of points whose orbit is bounded. The term "escape-time" is a bit of a misnomer since it applies to a common computer algorithm for generating images of such fractals, where points that are not in the fractal (they "escape") are colored by the length of the pre-escape orbit. Mathematically, points whose orbit is unbounded are simply not in the fractal.

One disadvantage of this categorization is that many fractals can be defined in different ways. For example, the Sierpinski gasket is easily defined using recursive geometric operations, by an IFS, or as an escape-time fractal. But perhaps this isn't too bad since computer-generated approximations using different methods are subtly different, even if the mathematical object is the same in all cases.

[masbicudo]

Tetration fractals: http://math.eretrandre.org/tetrationforum/showthread.php?tid=144

Collatz fractals: https://mathematica.stackexchange.com/questions/115562/fractal-plotting-for-the-collatz-fractal

[Chillheimer]

welcome to the forum &  thanks for the input!
into which category would you sort these two? both escape time fractals?