Fractal Music(?)

In the past, I have treated fractals visually. For instance, in my treatment of the Mandelbrot set, I chose points in the complex plane to represent pixels in an image, applied the iterative function \(z_{n+1} = z_{n}^2 + z_0\) to each of those points until the orbit escaped (or failed to escape after a fixed number of iterations), then colored the pixel based on the number of iterations applied before the orbit escaped. Another visual approach was to compute a large number of orbits and treat their traces like photons hitting a light sensor, thus creating nebulabrot images. I have recently started playing around with an entirely different idea: instead of using the orbits to compute values for pixels in an image, the orbits can be used to generate sound.

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It’s a ξ, See?

While looking for a dead-tree set of Russell and Whitehead’s Principia Mathematica, I came across a scanned version in the University of Michigan’s Historical Math Collection. Not quite what I wanted, but I was highly amused by the annotations on one of the blank pages near the front:

It seems that some poor student in the past was having trouble with his Greek, particularly with the lowercase letter ξ (xi). Since that little guy is the bane of my existence, I couldn’t help but chuckle at the struggles of a another.

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2014 Fields Medal

The International Congress of Mathematicians (ICM) announced the 2014 Fields Medal awardees last night. The Fields Medal is one of (if not the) most prestigious honors in the mathematical community—it is often portrayed as the “Nobel Prize of mathematics.” Of particular note this year is that a woman—Maryam Mirzakhani—has been honored for the first time in the nearly 80 year history of the award. Quanta Magazine has published a nice biographical sketch of Dr. Mirzakhani (as well as the other winners).

Mathematics is a field that has been historically dominated by men. This has been a self fulfilling prophecy—our society often tells young women that math isn’t for women (see, for instance, the Barbie doll who states “Math class is tough!” or the innumerable stories about women being advised to “consider ‘easier’ programs”) leading to women pursuing other courses of study, which in turn leads to an underrepresentation of women in mathematics, thereby reinforcing the perception that women can’t do math. Each of these factors needs to be addressed and I hope that Dr. Mirzakhani’s being honored in this manner will help with the misconception that women cannot do well in mathematics.

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Black Moon

I finished my masters a little more than a year ago and am starting a Ph.D. in two months. In the intervening year, I have done a little research, some teaching, and made the (very) occasional post here. I have also been reading for fun(!) which is something that I haven’t done for quite a long time.

I am currently reading Kenneth Calhoun’s Black Moon. I haven’t really gotten that far into it (according to my Kobo thingy, I am 22% of the way through the book), but the book is (thus far) quite fantastic. The scenario is intriguing and the style and subject matter complement each other quite well. Assuming that it continues to be as good as it has been so far, I might put in the first or second slot of “Xander’s Best Reads of 2014” (obviously, the most important literary award of the year). Of course, the book could fall off the rails in the closing act, and I am generally not one to gush about a work before getting to the end, but I just encountered an amazing bit of prose / blank verse that I thought worth sharing.

For context, the premise of the book is that nearly everyone has lost the ability to sleep. The world is slowly crumbling, and noöne really knows why. An explanation is offered, perhaps from a mind addled by sleeplessness:

MAYBE it was food becoming a prop for food, the rise of corn and its many guises maybe it was the fluoride in the water maybe the author of us all decided to see what would happen maybe it was a distant comet dusting us with its tail of poisoned ice the moon was having its revenge someone uttering a combination of syllables that should never be uttered maybe it was the kids who weren’t given a chance maybe it was the fingerfucking of the priests the rise of autotune the piracy the orgy of infringement all the bad books and movies the shift to decentralization the emergence of collective intelligence the flattening of the world. Maybe it was the turtle on whose back we all live slowly shifting its feet the Sasquatch sending out vibes sharks swimming far upstream the game we inhabit had a glitch.

Maybe the angel’s horn had finally been blown.

Cool, no?

UPDATE: I finished the book this afternoon. It is a remarkable work—definitely one of the (if not the) best books that I have read recently. Yes, the book is moody and depressing, but the construction of that mood is well-crafted and allows for a faint sliver of hope. I don’t really want to consider a full-on review of the book, but I would compare it favorably to the works of Stanisław Lem (the dream-like qualities of Solaris spring immediately to mind).

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Blue Clover - click to enlarge.  Warning:  the full sized image is about 16 MB.

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Vermilion Clover - click to enlarge.  Warning:  the full sized image is about 9.6 MB.

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LEGO Fractals

My daughter has recently started playing with DUPLO blocks pretty consistently, which has me thinking about LEGO—the toy of my youth (and hopefully her’s in a couple of years, too!). In some ways, LEGO is an ideal medium for exploring fractals. They are relatively cheap and ubiquitous, forgiving of errors as they pop right apart, and have give a wonderfully tactile experience. I suspect that they might be a really interesting tool to use in the classroom, as well, but I haven’t really thought much about that yet.

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Lunar Eclipse

A propos of nothing in particular, and with minimal commentary, a couple of pictures of last night’s lunar eclipse (rollover either picture for annotation or click for a larger version):

While the moon was lovely, the proximity of the eclipsed moon, Mars (upper right) and a bright blue star (Spica, I think) was magnificent. I don’t have the greatest camera in the world, but I am reasonably pleased with the above shot.

A tighter shot of the moon and Spica (?). If anyone can confirm for me that the star in the picture is Spica, I would be grateful—Google was only so helpful.

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In the last year, I have been pretty inactive here. On the other hand, I have been quite active in real life. Last November, I took a trip to the UK in order to present some of my work and to collaborate with some folk at the University of Warwick. The first result of that collaboration is the paper On the Assouad dimension of self-similar sets with overlaps, which has been submitted for publication.

In addition to spending some time on interesting problems, I have been teaching several sections of precalculus at UNR as an adjunct. While I recognize that my labour is being exploited, I really enjoy teaching and feel like I have finally gotten my trigonometry lectures down to something that are both engaging and instructive.

In other news, I have been offered (and accepted) a graduate student slot at the UC Riverside. I will be starting work towards a Ph.D. in mathematics in September. I am really excited about the work—there is a vibrant and active research community there with interests that seem to intersect my own quite well.

Finally, I have been playing with LEGOs. More on that later.

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Calculus I—Days 23 & 24

The term is rapidly drawing to a close, and I am beginning to feel just a little overwhelmed. Moreover, the class has finally hit a rhythm, and the things are mostly running smoothly, thus I have less to discuss in this space. For that reason, I am combining the posts for last Thursday and Friday.

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