## LaTeX forum ⇒ Graphics, Figures & Tables ⇒ Quadratic fractal with TikZ

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Tobias_G
Posts: 3
Joined: Sat May 04, 2013 5:27 pm

### Quadratic fractal with TikZ

Dear all,

I would like to create a fractal similar to the Koch snowflake using TikZ:

\documentclass{article}\usepackage{tikz}\usetikzlibrary{lindenmayersystems}\begin{document}\begin{tikzpicture}\draw [l-system={rule set={F -> F-F++F-F}, step=2pt, angle=60,    axiom=F++F++F, order=4}] lindenmayer system -- cycle;\end{tikzpicture}\end{document}

What do I have to change in the code above so that the outcome looks like the attached graphic? (One starts with a square of sidelength 1, then one attaches in the middle of each side a new square with sidelength 1/3 and so on...)

Thanks for your help!
Attachments
quadrat_fraktal.png (6.52 KiB) Viewed 3871 times
Last edited by cgnieder on Mon May 06, 2013 9:54 am, edited 2 times in total.
Reason: inline code changed to code block, scaled image so it can also be viewed on small screens

Tags:

Stefan Kottwitz
Posts: 9572
Joined: Mon Mar 10, 2008 9:44 pm
Hi Tobias,

the fractal image is built of 4 identical parts, so generate the basic part and built it together by an axiom like F+F+F+F with an angle of 90 degrees.

In contrast to the Koch snowflake, not each line is recursively replaced. This can be solved using two different rules.

So here's an approach:

\documentclass{article}\usepackage{tikz}\usetikzlibrary{lindenmayersystems}\begin{document}\begin{tikzpicture}   \draw [l-system={rule set={G -> F-G+G+G-F, F -> FF}, step=2pt, angle=90,          axiom=G+G+G+G, order=3}] lindenmayer system -- cycle;\end{tikzpicture}\end{document}

The versions up to level 4, scaling omitted:

fractal.png (3.79 KiB) Viewed 3893 times

It still seems to need a bit of adjusting line lengths, to exact match the image.

Stefan

Tobias_G
Posts: 3
Joined: Sat May 04, 2013 5:27 pm
Hi Stefan,

thank you very much for your quick an enlightening response!

How can I adjust the line lengths?

Tobias

Stefan Kottwitz
Posts: 9572
Joined: Mon Mar 10, 2008 9:44 pm
Another rule is useful here:

\draw [l-system={rule set={G -> F-G+G+G-F, F -> FFH, H -> FF}, step=2pt, angle=90,        axiom=G+G+G+G, order=3}] lindenmayer system -- cycle;

Tested with order 3 and 5 (used \begin{tikzpicture}[scale=0.40,transform shape] to scale it down then)
square-fractal.png (4.72 KiB) Viewed 3874 times

Stefan

Tobias_G
Posts: 3
Joined: Sat May 04, 2013 5:27 pm
Stefan,

you are a LaTeX-BOSS !

Thank you so much for your help.
Tobias