Very simple formula for fractal patterns

[Alef]

In wikipedia I found this fractal I never heard about, but it looks intriguing square pattern, somewhat like ducks/kalisets:
A Fibonacci word fractal by Samuel Monnier

[kram1032]

Forumla/Link?

[s31415]

Hi,

The Fibonacci fractal was studied by Alexandre Monnerot-Dumaine, see this article:
http://hal.archives-ouvertes.fr/hal-00367972/fr/
Concerning my image above, I explained the idea behind the algorithm here:
http://algorithmic-worlds.net/blog/blog.php?Post=20090802
This algorithm essentially piles squares to draw it, but it is not the most natural way to draw it, see the article.

Best,

Sam

[LMarkoya]

FIrstly I want to say how glad I am to have found this thread today, while started some time ago it is a great reminder of the fractal genius that lis within the forums here.....being an artist and not a mathematician, I love the work you have all done here and really find it very stimulating. One day I hopwe I can steal some stem cells from Pablo and many others here to try to understan all this and implement it in my art.

Friday April 28th, 2013 9:15 EST, my hat is off to you all

[cKleinhuis]

and this might be interesting as well, a collection of sams formulas in ultrafractal wiki:
http://ultrafractalwiki.fractalforums.com/Gallery_for_Samuel_Monnier%27s_Formulas

[Alef]

Random? -   Lucky
      /
Talis - Ducky - Ducks  - Kalisets
      I   |
   Mandelbox -   Amazing Surface 

Ed Algra uploaded some new version of Ducky a Lucky. Sounds as random numbers involved but it kind of interesting coz it started with ducky.