Making Stuff pt. 1

So I’m on summer break right now, its been relaxing, or at least more relaxing than not summer break.  Unlike the other four breaks Sugar and I have had in the past year, we’ve elected to not take any major adventures, but instead stay in Seattle and geocache (even though we’ve only found two so far) and maybe take some smaller adventures (zero so far–well, except for Rikki’s birthday and the Enchantments).  My gig schedule has died down big time, I don’t have anything else going on for the rest of the month.

We have been making things, though.  Part one will be the computer edition.  I haven’t gotten much better at programming since I started, but I can at least make things happen.

In the 1950’s and 60’s, there was a school of composers led by Arnold Schoenberg, which composed with a technique called serialism.  In this mode, the composer makes what are called tone-rows where you are not allowed to repeat a note until you have stated all twelve.  For example: [E F Bb A G Db Eb C B Ab D Gb].  This would be the basis for the composition along with inversions, transpositions, retrogrades, and all other sorts of transformations you can come up with.  I had a conversation with a friend who has explored taking this idea a step further: what if you could write a tone row where not only the notes are not repeated, but the intervals between the notes are not repeated?  I have since become aware that this is actually a thing (::see here::), but I wrote a program to generate a list of all possible rows described.

I didn’t count them but there are more than just a few possibilities.  How cool.  Here is my code:

Code to find All tone-interval Rows
Code to find All tone-interval Rows

The second programming adventure I’ve been on is to plot the ::Mandelbrot Set::.  The idea is this: take a complex number, call it c.  Let z_0 = c.  Let z_1 = (z_0)^2 + c.  Let z_2 = (z_1)^2 + c, and so on and so forth.  You end up with a list of complex numbers z_0, z_1, z_2, …

The point c is in the Mandelbrot set if the sequence that it generates does not fly off to infinity, and instead stays close to the origin.  The set is actually a fractal, and a ::pretty crazy one::

I have written programs in the past to test whether a point is in the set or not, but I recently learned how to use graphics to draw a picture of the thing.  Here are the results.  I’ve left off a bit of the code that defines what complex number arithmetic looks like, but it should be clear from my descriptions what I’m talking about

Plots a picture of the Mandelbrot Set
Plots a picture of the Mandelbrot Set

Mandelbrot Set

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