Graphics, Figures & Tables ⇒ tikZ | Koch Snowflake

[svend_tveskaeg]

Hi all.

Consider the following MWE, which I found here:

Code: Select all

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.fractals}
\begin{document}
\begin{tikzpicture}[decoration=Koch snowflake]
    \draw decorate{ decorate{ decorate{ decorate{ (0,0) -- (3,0) }}}};
\end{tikzpicture}
\end{document}

How do I extend it in order to draw the entire fractal?

Thank you in advance!

P.S. I have never used TikZ before.

[Stefan Kottwitz]

Hi,

decorate a longer path. Here I use angles and relative coordinates:

Code: Select all

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.fractals}
\begin{document}
\begin{tikzpicture}[decoration=Koch snowflake]
  \draw decorate{ decorate{ decorate{ decorate{
       (0,0) -- ++(60:3)  -- ++(300:3) -- ++(180:3)}}}};
\end{tikzpicture}
\end{document}

snowflake.png (6.17 KiB) Viewed 12475 times

Stefan

[svend_tveskaeg]

Spot on! Thank you!

[Stefan Kottwitz]

You could also use the lindenmayersystems library. Here's an example with additional color shading, which I posted on my TeX blog:

Code: Select all

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{lindenmayersystems}
\usetikzlibrary[shadings]
\begin{document}
\begin{tikzpicture}
\shadedraw[shading=color wheel] 
  [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}

koch-snowflake.png (8.52 KiB) Viewed 12474 times

More of this: Lindenmayer systems with TikZ.

Stefan

[svend_tveskaeg]

Thank you!

I did notice this example at first, but I would like the drawing to be "clean". Therefore, I chose the colorless snowflake.

[Stefan Kottwitz]

No problem, the shading was just a fancy addition. You could use a normal \draw.

Code: Select all

\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}

koch.png (3.93 KiB) Viewed 12465 times

With the L-System syntax we could draw various fractals, both well known as the Sierpinski gasket, the space-filling fractals Pascal curve and Hilbert curve, but many more also unknown trees, farns and other plan structures, ornaments, and more.

Stefan

[svend_tveskaeg]

Arrrh! I see.

Then I will implement that instead.

Thank you for the hint(s)!