resources
visualizations
presentations
lunch break
Distractions and amusements, with a sandwich and coffee.
data visualization + art
Hola Mundo and Hello `\pi`
Art is science in love.
— E.F. Weisslitz
art and algorithms
Some algorithms connect us and some keep us apart—we need them to remind us what it is to be human and what it is to be a computer.
My cover design for Hannah Fry's Hello World: Being Human in the Age of Algorithms is based on my 2013 `\pi` Day art. The book is published by Blackie Books.
creating the cover
The cover begins with a 57 × 35 matrix of 1,995 colored circles. Each circle encodes a digit of `\pi`, starting with 3.1415.... Inside each circle is a smaller circle whose color is based on the next digit. The radius of the inner circle is `1/\phi^2` where `1/\phi = 0.618` is the Golden Ratio.
Once the circles are drawn, neighbouring circles that correspond to the same digit are connected with thick lines. The thickness of these lines is `t_0 = 3/(2\phi^2)`, relative to the outer circle radius. Circles that correspond to digits whose difference is `1` or `-1` are connected by a slightly thinner line with thickness `t_1 = t_0/\phi`.
More lines are drawn that connect digits with a larger difference, `|d| > 1`. The thickness for these lines is `t_d = t_0/\phi^{|d|}`. When all differences up to `|d| < 6` are accounted for, we get a pleasant jumble of lines.
To accommodate the title and other text on the cover, the design was generated by avoiding drawing any circles within a certain distance of the text.
This way, the network of digits wraps around the text. In the final design, the front page has 1,418 digits and the back has 878 digits.
cover remixes
just the lines
news + thoughts
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.
1-bit zoomable gigapixel maps of Moon, Solar System and Sky
Places to go and nobody to see.
Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.
Quantile regression
Quantile regression robustly estimates the typical and extreme values of a response.Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"
Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.
Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.
Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.
Background reading
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.