Fractal Typography

(Sierpinski, Knuth, memes, and a Turning complete system)


Travis Hoppe

https://github.com/thoppe/fractal_typography

Donald Knuth created TeX; wrote a a diatribe on the shape of .



Used by physicists & mathematicians to make
beautiful equations and academic papers.

Fractals

self-similar patterns governed by a rule


Fractals via memes

the inception argument


Fractals + typography = ?

Sierpinski's carpet

will be our "template"

Source image

Compile and repeat

Used pdflatex to compile and copy the result back into source.pdf.



\documentclass{standalone}
\usepackage{graphicx}
\newcommand{\A}{\á¼°ncludegraphics{pdf/source}}
...    
\begin{document}
\begin{center}
\begin{tabular}{lll}
\A & \A & \A\\
\A &    & \A\\
\A & \A & \A
\end{tabular}
\end{center}
\end{document}

Level 2 (8 copies)

Level 3 (512 copies)

Level 4 (4096 copies)

Level 5 (32768 copies)

Level 6 (262144 copies)


crashes my PDF viewer


used to crash Google Docs (funny story...)


...


Can we go deeper?

How big are the files?

compiled to depth 1000


-rw-r--r-- 1 hoppeta hoppeta 27664 Dec  8 13:52 level_001.pdf
-rw-r--r-- 1 hoppeta hoppeta 28753 Dec  8 13:52 level_002.pdf
-rw-r--r-- 1 hoppeta hoppeta 29132 Dec  8 13:52 level_003.pdf
-rw-r--r-- 1 hoppeta hoppeta 29539 Dec  8 13:52 level_004.pdf
-rw-r--r-- 1 hoppeta hoppeta 29938 Dec  8 13:52 level_005.pdf
-rw-r--r-- 1 hoppeta hoppeta 30338 Dec  8 13:52 level_006.pdf
...
-rw-r--r-- 1 hoppeta hoppeta 431996 Dec  8 11:10 level_999.pdf

Not exponential growth...?

How much information?

only 41 unique bytes per level! (FYI PDF's are Turing complete)

Thanks, you!

Tweet thoughts to @metasemantic!