möchte­gern­geek

Nightmare before Easter

de Code Code Python

Easter is a holiday whose time is determined with an unnecessarily complicated rule. The first Sunday after the first full moon in Spring. Most people have no other choice than to look its date up in a calendar and trust in the calendar manufacturer. But not anymore! I will stick it to Big Calendar and reveal the secret formula to calculate the date of easter!

from datetime import date

def easter(year: int) -> date:
    y = year
    g = y % 19 + 1                    # golden number
    c = y // 100 + 1                  # century
    x = (3 * c) // 4 - 12             # correction: dropped leap years
    z = (8 * c + 5) // 25 - 5         # correction: synchronize with moon's orbit
    d = (5 * y) // 4 - x - 10         # find sunday
    e = (11 * g + 20 + z - x) % 30    # epact
    if e == 25 and g > 11 or e == 24:
        e += 1
    n = 44 - e                        # full moon in march
    if n < 21:
        n += 30
    n = n + 7 - (d + n) % 7           # advance to next sunday
    month, day = (4, n - 31) if n > 31 else (3, n)

    return date(year, month, day)

My favorite thing about it is that each line becomes more horrendous than the previous.

This algorithm was developed by Lilius and Clavius at the end of the 16th Century. I became aware of it through a mention in an exercise in Donald Knuth’s The Art of Computer Programming 1 (Third edition, p. 159f).

Twitter Profile Background Colors

de Code Code Image Python Twitter

I collected tweets of \(>8'000'000\) Twitter users for an academic project. But Twitter does not only give you the tweets, but also many more data like the profile background color of users. It would be a shame to let these data go to waste, so I decided to process them into digital art. I wanted to show all the colors in one picture and group similar colors close to each other. This turned out to be much less trivial than I expected, since the space in which the colors live is the three dimensional RGB cube, but my image is only two dimensional. There is no “correct” way to project the colors down.

Here, I decided to put a 2D Hilbert curve through the image and paint the colors in the order they are encountered by a 3D Hilbert curve in the RGB cube. Ignoring the two default colors #F5F8FA and #C0DEED, this produces this image:

Twitter profile background colors

And thanks to the Python packages hilbertcurve and pypng the code needed to generate this image is quite harmless:

from math import ceil, sqrt, log2

from hilbertcurve.hilbertcurve import HilbertCurve
import png


"""
    turn an RGB string like `#C0DEED` into a tuple of integers,
    i.e., coordinates of the RGB cube
"""
def str2rgb(s):
    s = s.strip("#")
    return (int(s[0:2], 16), int(s[2:4], 16), int(s[4:6], 16))


"""
    `color_histogram` is a dict mapping an rgb string like `#F5F8FA`
    to the number of usages of this color
"""
def plot_background_colors(color_histogram, filename="colors.png"):
    defaults = {"F5F8FA", "C0DEED"}

    data = {str2rgb(rgb): d for rgb, d in color_histogram if rgb not in defaults}

    # calculate the size of the resulting image
    # for a 2D Hilbert curve, it mus be square with a width, which is a power of 2
    num_pixels = sum(data.values())
    min_width = ceil(sqrt(num_pixels))
    exponent = ceil(log2(min_width))
    width = 2**exponent

    # output buffer for a `width x width` png, with 4 color values per pixel
    buf = [[0 for _ in range(4 * width)] for _ in range(width)]

    hc2 = HilbertCurve(exponent, 2)
    # there are 256 = 2^8 values in each direction of the RGB cube
    hc3 = HilbertCurve(8, 3)

    sorted_rgbs = sorted(data.keys(), key=lambda x: hc3.distance_from_point(x))

    idx = 0
    for rgb in sorted_rgbs:
        for _ in range(data[rgb]):
            # get the coordinate of the next pixel
            x, y = hc2.point_from_distance(idx)
            # assign the RGBA values to the pixel
            buf[x][4 * y] = rgb[0]
            buf[x][4 * y + 1] = rgb[1]
            buf[x][4 * y + 2] = rgb[2]
            buf[x][4 * y + 3] = 255

            idx += 1

    png.from_array(buf, 'RGBA').save(filename)

The input histogram was in my case just a simple SQL query away:

SELECT profile_background_color, COUNT(profile_background_color) FROM users
    GROUP BY profile_background_color;