syncopation & accordionlike France, but no dog poopmore quotes

# making poetry out of spam is fun

In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017

# visualization + design

The 2018 Pi Day art celebrates the 30th anniversary of $\pi$ day and connects friends stitching road maps from around the world. Pack a sandwich and let's go!

# $\pi$ Approximation Day Art Posters

2018 $\pi$ day shrinks the world and celebrates road trips by stitching streets from around the world together. In this version, we look at the boonies, burbs and boutique of $\pi$ by drawing progressively denser patches of streets. Let's go places.
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

The never-repeating digits of $\pi$ can be approximated by $22/7 = 3.142857$ to within 0.04%. These pages artistically and mathematically explore rational approximations to $\pi$. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: $\pi$ approximation day!

Want more math + art? Discover the Accidental Similarity Number. Find humor in my poster of the first 2,000 4s of $\pi$.

The $22/7$ approximation of $\pi$ is more accurate than using the first three digits $3.14$. In light of this, it is curious to point out that $\pi$ Approximation Day depicts $\pi$ 20% more accurately than the official $\pi$ Day! The approximation is accurate within 0.04% while 3.14 is accurate to 0.05%.

## first 10,000 approximations to $\pi$

For each $m=1...10000$ I found $n$ such that $m/n$ was the best approximation of $\pi$. You can download the entire list, which looks like this

$m n m/n relative_error best_seen? 1 1 1.000000000000 0.681690113816 improved 2 1 2.000000000000 0.363380227632 improved 3 1 3.000000000000 0.045070341449 improved 4 1 4.000000000000 0.273239544735 5 2 2.500000000000 0.204225284541 7 2 3.500000000000 0.114084601643 8 3 2.666666666667 0.151173636843 9 4 2.250000000000 0.283802756086 10 3 3.333333333333 0.061032953946 11 4 2.750000000000 0.124647812995 12 5 2.400000000000 0.236056273159 13 4 3.250000000000 0.034507130097 improved 14 5 2.800000000000 0.108732318685 16 5 3.200000000000 0.018591635788 improved 17 5 3.400000000000 0.082253613025 18 5 3.600000000000 0.145915590262 19 6 3.166666666667 0.007981306249 improved 20 7 2.857142857143 0.090543182332 21 8 2.625000000000 0.164436548768 22 7 3.142857142857 0.000402499435 improved 23 7 3.285714285714 0.045875340318 24 7 3.428571428571 0.091348181202 ... 354 113 3.132743362832 0.002816816734 355 113 3.141592920354 0.000000084914 improved 356 113 3.150442477876 0.002816986561 ... 9998 3183 3.141061891298 0.000168946885 9999 3182 3.142363293526 0.000245302310 10000 3183 3.141690229343 0.000031059327$

As the value of $m$ is increased, better approximations are possible. For example, each of $13/4$, $16/5$, $19/6$ and $22/7$ are in turn better approximations of $\pi$. The line includes the $improved$ flag if the approximation is better than others found thus far.

## next best after 22/7

After $22/7$, the next better approximation is at $179/57$.

Out of all the 10,000 approximations, the best one is $355/113$, which is good to 7 digits (6 decimal places).

$pi = 3.1415926 355/113 = 3.1415929$

I've scanned to beyond $m=1000000$ and $355/113$ still remains as the only approximation that returns more correct digits than required to remember it.

## increasingly accurate approximations

Here is a sequence of approximations that improve on all previous ones.

$1 1 1.000000000000 0.681690113816 improved 2 1 2.000000000000 0.363380227632 improved 3 1 3.000000000000 0.045070341449 improved 13 4 3.250000000000 0.034507130097 improved 16 5 3.200000000000 0.018591635788 improved 19 6 3.166666666667 0.007981306249 improved 22 7 3.142857142857 0.000402499435 improved 179 57 3.140350877193 0.000395269704 improved 201 64 3.140625000000 0.000308013704 improved 223 71 3.140845070423 0.000237963113 improved 245 78 3.141025641026 0.000180485705 improved 267 85 3.141176470588 0.000132475164 improved 289 92 3.141304347826 0.000091770575 improved 311 99 3.141414141414 0.000056822190 improved 333 106 3.141509433962 0.000026489630 improved 355 113 3.141592920354 0.000000084914 improved$

For all except one, these approximations aren't all good value for your digits.

For example, $179/57$ requires you to remember 5 digits but only gets you 3 digits of $\pi$ correct (3.14).

Only $355/113$ gets you more digits than you need to remember—you need to memorize 6 but get 7 (3.141592) out of the approximation!

You could argue that $22/7$ and $355/113$ are the only approximations worth remembering. In fact, go ahead and do so.

## approximations for large $m$ and $n$

It's remarkable that there is no better $m/n$ approximation after $355/113$ for all $m \le 10000$.

What do we find for $m > 10000$?

Well, we have to move down the values of $m$ all the way to 52,163 to find $52163/16604$. But for all this searching, our improvement in accuracy is miniscule—0.2%!

$pi 3.141592653589793238 m n m/n relative_error 355 113 3.1415929203 0.00000008491 52163 16604 3.1415923873 0.00000008474$

After 52,162 there is a slew improvements to the approximation.

$104348 33215 3.1415926539 0.000000000106 208341 66317 3.1415926534 0.0000000000389 312689 99532 3.1415926536 0.00000000000927 833719 265381 3.141592653581 0.00000000000277 1146408 364913 3.14159265359 0.000000000000513 3126535 995207 3.141592653588 0.000000000000364 4272943 1360120 3.1415926535893 0.000000000000129 5419351 1725033 3.1415926535898 0.00000000000000705 42208400 13435351 3.1415926535897 0.00000000000000669 47627751 15160384 3.14159265358977 0.00000000000000512 53047102 16885417 3.14159265358978 0.00000000000000388 58466453 18610450 3.14159265358978 0.00000000000000287$

I stopped looking after $m=58,466,453$.

Despite their accuracy, all these approximations require that you remember more or equal the number of digits than they return. The last one above requires you to memorize 17 (9+8) digits and returns only 14 digits of $\pi$.

The only exception to this is $355/113$, which returns 7 digits for its 6.

You can download the first 175 increasingly accurate approximations, calculated to extended precision (up to $58,466,453/18,610,450$).

VIEW ALL

# Molecular Case Studies Cover

Fri 06-07-2018

The theme of the April issue of Molecular Case Studies is precision oncogenomics. We have three papers in the issue based on work done in our Personalized Oncogenomics Program (POG).

The covers of Molecular Case Studies typically show microscopy images, with some shown in a more abstract fashion. There's also the occasional Circos plot.

I've previously taken a more fine-art approach to cover design, such for those of Nature, Genome Research and Trends in Genetics. I've used microscopy images to create a cover for PNAS—the one that made biology look like astrophysics—and thought that this is kind of material I'd start with for the MCS cover.

Cover design for Apr 2018 issue of Molecular Case Studies. (details)

# Happy 2018 $\tau$ Day—Art for everyone

Wed 27-06-2018
You know what day it is. (details)

# Universe Superclusters and Voids

Mon 25-06-2018

A map of the nearby superclusters and voids in the Unvierse.

By "nearby" I mean within 6,000 million light-years.

The Universe — Superclustesr and Voids. The two supergalactic hemispheres showing Abell clusters, superclusters and voids within a distance of 6,000 million light-years from the Milky Way. (details)

# Datavis for your feet—the 178.75 lb socks

Sat 23-06-2018

In the past, I've been tangentially involved in fashion design. I've also been more directly involved in fashion photography.

It was now time to design my first ... pair of socks.

Some datavis for your feet: the 178.75 lb socks. (get some)

In collaboration with Flux Socks, the design features the colors and relative thicknesses of Rogue olympic weightlifting plates. The first four plates in the stack are the 55, 45, 35, and 25 competition plates. The top 4 plates are the 10, 5, 2.5 and 1.25 lb change plates.

The perceived weight of each sock is 178.75 lb and 357.5 lb for the pair.

The actual weight is much less.

# Genes Behind Psychiatric Disorders

Sun 24-06-2018

Find patterns behind gene expression and disease.

Expression, correlation and network module membership of 11,000+ genes and 5 psychiatric disorders in about 6" x 7" on a single page.

Design tip: Stay calm.

An analysis of dust reveals how the presence of men, women, dogs and cats affects the variety of bacteria in a household. Appears on Graphic Science page in December 2015 issue of Scientific American.

More of my American Scientific Graphic Science designs

Gandal M.J. et al. Shared Molecular Neuropathology Across Major Psychiatric Disorders Parallels Polygenic Overlap Science 359 693–697 (2018)

# Curse(s) of dimensionality

Tue 05-06-2018
There is such a thing as too much of a good thing.

We discuss the many ways in which analysis can be confounded when data has a large number of dimensions (variables). Collectively, these are called the "curses of dimensionality".

Nature Methods Points of Significance column: Curse(s) of dimensionality. (read)

Some of these are unintuitive, such as the fact that the volume of the hypersphere increases and then shrinks beyond about 7 dimensions, while the volume of the hypercube always increases. This means that high-dimensional space is "mostly corners" and the distance between points increases greatly with dimension. This has consequences on correlation and classification.

Altman, N. & Krzywinski, M. (2018) Points of significance: Curse(s) of dimensionality Nature Methods 15:399–400.