journal entry #2034

GUILLOCHÉ PATTERNS: A GLORIFIED SECURITY MEASURE.

    The simple yet invariably intricate interaction between computer code and an unfiltered creativity with Euclidean geometry have rendered the geometric lathes of the 19th century obsolete. Just about anybody versed with the language of computers or Adobe Illustrator can produce what would have taken hours in a mere thirty minutes. Shockingly enough, it is those things, that being what we call “Guilloché patterns”, that line the edges of our currency, passports, and just about anything else that is subject to artistic forgery.

    The code I’ve written is centered around a series of functions written in a non-multivariable manner. In this example, I utilized two functions with a bicentric focus: “radius” and “cam”. “Radius” controls what I will call the “hidden” circle aspect––rada in the function. These circles are of number n (depending on your own complex taste) and are centered around the same fixed point, rotating about that point simultaneously. “Cam”, on the other hand, is comprised of a set of circles of their own unique radii––radb, radc, radd, and so on. These functions can be edited so as to produce more circles, thereby producing a more fuller (that is, more circular) end product.

   To produce the patterns as provided later in the paper, the following functions were used:

x = xorg + (rada + radb) * cos(i) + b * cos(((rada + radb) / radb) * i) + c * cos(((rada + radc) / radc) * i) + d * cos(((rada + radd) / radd) * i) + e * cos(((rada + rade) / rade) * i)

y = yorg - (rada + radb) * sin(i) - b * sin(((rada + radb) / radb) * i) - c * sin(((rada + radc) / radc) * i) - d * sin(((rada + radd) / radd) * i) - e * sin(((rada + rade) / rade) * i)

    However, if these patterns were to be replicated within the third dimension, I imagine the function to look something of or similar to:

z = zorg - (rada + radb) * tan(i) - b * tan(((rada + radb) / radb) * i) - c * tan(((rada + radc) / radc) * i) - d * tan(((rada + radd) / radd) * i) - e * tan(((rada + rade) / rade) * i)

   I added a slider to my program so as to maximize easy usage, as well as to observe the differences between increasing/decreasing steps in the magnitude of the radii. Here are a few typical renders of the patterns that I generated myself with this program:

    Perhaps it may be of surprise when I reveal that I am not the most talented when it comes to computer science––these functions manifested from a mere three day autodidactic episode with books purchased from my local bookstore. That being said, a call for a refreshing and novel way to protect significant government particulars is not one of blasphemy. If someone as inexperienced (and invariably over-the-top, what with the amount of circles I added in the previous outputs) as myself managed to conjure up patterns that have a high chance of appearing on the Brazilian Real, perhaps a change in security, one that can’t be produced by technological intelligence or pure artistry, isn’t as outrageous as it sounds.

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I stabbed my geometry homework and it was very graphic