There are levels of tidiness.

Tidy.
Very Tidy.
Totally Deranged Tidy.

Geeky Tidy.

After sharing these awesome pictures by the Swiss “artist” Ursus Wehrli with the world, Martin N. pointed out that there is still a severe issue with the Badewiese: People are not even sorted by the colors of their swimsuits! Adding to that, trees are placed in total chaos, not to speak of their leaves; clearly, there are tiny waves on the water; and one can almost see blades of grass not being sorted by size. Obviously, this picture needed further tidying up.

© Ursus Wehrli

Python to the rescue! 5 minutes, 10 lines, and half a beer later I had a program that would load the image, re-arrange its pixels, and save it again:

from PIL import Image

old = Image.open("tidy.jpg")
colors = old.getcolors(old.size[0] * old.size[1])
data = []
for count, color in colors:
    data.extend(count * [color])
data.sort()
new = Image.new('RGB', old.size)
new.putdata(data)
new.save("naive_tidy.png")

This yields the following picture:

So how was this “re-arrangement” performed? In a naïve approach, I just sorted the RGB values of the pixels, which is why there are many consecutive lines (of equal reds) with abrupt changes. Ordered, but far from being tidy.

Let’s try another color space and sort by HSV values—a smooth hue should look better, after all. So by adding

import colorsys

and changing one line to

data.sort(key=lambda rgb: colorsys.rgb_to_hsv(*rgb))

we get the following image:

More beautiful, but the red and white noise in the end doesn’t look tidy at all. We want a smooth transition through all given colors. Hilbert curves to the rescue! Found a ready-to-be-used Hilbert walk implementation, added

import hilbert

and changed the sorting once again to

data.sort(key=hilbert.Hilbert_to_int)

to get this image:

Mathematical computer science just made the world a little tidier.

After the official part of the conference, I stayed the rest of the week and further explored Amsterdam. Went to the zoo with Daniel Krenn, who happened to be in Amsterdam over the long weekend as well, and visited the Van Gogh Museum. Met my Dutch Erasmus buddies Lyor and Joost on Saturday. See some pictures below.

If you wonder what Mathics is: it’s a general-purpose computer algebra system implementing the awesome Mathematica mathematics/programming language. Some of its most important features are

• a powerful functional programming language,
• a system driven by pattern matching and rules application,
• rationals, complex numbers, and arbitrary-precision arithmetic,
• lots of list and structure manipulation routines,
• an interactive graphical user interface right in the Web browser using MathML (apart from a command line interface),
• creation of graphics (e.g. plots) and display in the browser using SVG,
• an online version at www.mathics.net for instant access,
• export of results to LaTeX (using Asymptote for graphics),
• a very easy way of defining new functions in Python,
• an integrated documentation and testing system.

Read the manual to learn more about the over 350 built-in functions and symbols in Mathics.

The actual heavy math stuff (like integration) is mostly done by the Python package SymPy. There is optional support for functions depending on Sage as well. Despite “out-sourcing” most mathematical functions, Mathics has more than 20,000 lines of Python code already, dealing with much non-trivial stuff such as parsing Mathematica input, pattern matching, graphics generation, etc.

Unfortunately, Firefox is the only browser supported so far, because no other browser supports MathML yet. However, this is expected to change pretty soon when Webkit (used by Safari and Chrome) adds MathML support. I wonder whether Internet Explorer will ever get that far.

I set up a project homepage at www.mathics.org for organizational stuff, while www.mathics.net is still the place for the online interface of Mathics. The source code is hosted at github.

I hope that one day there will be developers joining me. Contact me if you want to get involved!