resources
visualizations
presentations
lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
`\pi` Day 2014 Art Posters
On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.
For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong. I sympathize with this position and have `\tau` day art too!
If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!
Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.
For the 2014 `\pi` day, two styles of posters are available: folded paths and frequency circles.
The folded paths show `\pi` on a path that maximizes adjacent prime digits and were created using a protein-folding algorithm.
The frequency circles colourfully depict the ratio of digits in groupings of 3 or 6. Oh, look, there's the Feynman Point!
frequency circles of `pi`
Some of the posters for this year's Pi Day art expand on the work from last year, which showed Pi as colored circles on a grid.
For those of you who really liked this minimalist depiction of π , I've created something slightly more complicated, but still stylish: Pi digit frequency circles. These are pretty and easy to understand. If you like random distribution of colors (and circles), these are your thing.
Briefly, each set of concentric rings corresponds to a sequence of digits in
π
, such as 3 (314 159 265 ...) or 6 (314159 265358 ...). The number of times a given digit is seen within a sequence is encoded by the thickness of the ring. Rings are ordered outward in numerical order of their digits (i.e. 0 on the inside, 9 on the outside).
For some posters, the first digit (3) is offset from the rest of the groups. Look for the high count of 9s at the end of posters showing π up to the Feynman Point (6 9s at digit 762). For posters that show more digits, try to find the Feynman Point somewhere among the groups.
The Feynman point is at an extremely interesting location. If we group the digits of
π
into groups of 6, then the first 999999 falls exactly into the 128th group. But, if we group the digits by 3s, then the two groups 999 and 999 fall exactly into groups 255 and 256 (a power of 2!), which can be arranged into a perfect square of 16 x 16 groups.
The Feynman point is a specific case of the general case in which the digit d appears n times in a row. I call this the (d=7,n=6) and provide a list of all these points in the first 1,000,000 digits. Points with a large n value will contribute significantly to the frequency distribution of the digit group they fall in. If the sequence is split across groups, its impact is lower.
news + thoughts
Genome Sciences Center 20th Anniversary Clothing, Music, Drinks and Art
Science. Timeliness. Respect.
Read about the design of the clothing, music, drinks and art for the Genome Sciences Center 20th Anniversary Celebration, held on 15 November 2019.
As part of the celebration and with the help of our engineering team, we framed 48 flow cells from the lab.
Each flow cell was accompanied by an interpretive plaque explaining the technology behind the flow cell and the sample information and sequence content.
Scientific data visualization: Aesthetic for diagrammatic clarity
The scientific process works because all its output is empirically constrained.
My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.
Yearning for the Infinite — Aleph 2
Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).
I discuss the math behind the video and the system I built to create the video.
Hidden Markov Models
Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte
A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.
Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.
In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.
We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.
Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. Nature Methods 16:795–796.
Background reading
Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.
Hola Mundo Cover
My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.
Curious how the design was created? Read the full details.
Markov Chains
You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts
A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.
Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.
Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.
This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.
Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.