visualization + design
Hilbert Curve Art, Hilbertonians and Monkeys
I collaborated with Scientific American to create a data graphic for the September 2014 issue. The graphic compared the genomes of the Denisovan, bonobo, chimp and gorilla, showing how our own genomes are almost identical to the Denisovan and closer to that of the bonobo and chimp than the gorilla.
Here you'll find Hilbert curve art, a introduction to Hilbertonians, the creatures that live on the curve, an explanation of the Scientific American graphic and downloadable SVG/EPS Hilbert curve files.
Hilbert curve art posters
There are wheels within wheels in this village and fires within fires!
— Arthur Miller (The Crucible)
Recursive art. Same line. A variety of styles. Font is Gotham Light.
You can download the basic curve shapes for orders 1 to 10 and experiment yourself. Both square and circular forms are available.
Hilbert curve rugs, orders 1–10
Just add tassles and lose yourself in 10 levels of recursion.
The rugs are made up of 10 overlapping Hilbert curves of order 1–10.
| order | points | segments | length |
| `n` | `4^n` | `4^{n-1}` | `2^n-2^{-n}` |
| 1 | 4 | 3 | 1.5 |
| 2 | 16 | 15 | 3.75 |
| 3 | 64 | 63 | 7.875 |
| 4 | 256 | 255 | 15.9375 |
| 5 | 1,024 | 1,023 | 31.96875 |
| 6 | 4,096 | 4,095 | 63.984375 |
| 7 | 16,384 | 16,383 | 127.9921875 |
| 8 | 65,536 | 65,535 | 255.99609375 |
| 9 | 262,144 | 262,143 | 511.998046875 |
| 10 | 1,048,576 | 1,048,575 | 1023.9990234375 |
The entire rug has 1,398,100 points and 1,398,090 segments of length 2045.0009765625. Length is expressed in units of the rug's side.
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Neural network primer
Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon
In the first of a series of columns about neural networks, we introduce them with an intuitive approach that draws from our discussion about logistic regression.
Simple neural networks are just a chain of linear regressions. And, although neural network models can get very complicated, their essence can be understood in terms of relatively basic principles.
We show how neural network components (neurons) can be arranged in the network and discuss the ideas of hidden layers. Using a simple data set we show how even a 3-neuron neural network can already model relatively complicated data patterns.
Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20.
Background reading
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.
Cell Genomics cover
Our cover on the 11 January 2023 Cell Genomics issue depicts the process of determining the parent-of-origin using differential methylation of alleles at imprinted regions (iDMRs) is imagined as a circuit.
Designed in collaboration with with Carlos Urzua.
Akbari, V. et al. Parent-of-origin detection and chromosome-scale haplotyping using long-read DNA methylation sequencing and Strand-seq (2023) Cell Genomics 3(1).
Browse my gallery of cover designs.
Science Advances cover
My cover design on the 6 January 2023 Science Advances issue depicts DNA sequencing read translation in high-dimensional space. The image showss 672 bases of sequencing barcodes generated by three different single-cell RNA sequencing platforms were encoded as oriented triangles on the faces of three 7-dimensional cubes.
More details about the design.
Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9.
Browse my gallery of cover designs.
Regression modeling of time-to-event data with censoring
If you sit on the sofa for your entire life, you’re running a higher risk of getting heart disease and cancer. —Alex Honnold, American rock climber
In a follow-up to our Survival analysis — time-to-event data and censoring article, we look at how regression can be used to account for additional risk factors in survival analysis.
We explore accelerated failure time regression (AFTR) and the Cox Proportional Hazards model (Cox PH).
Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Regression modeling of time-to-event data with censoring. Nature Methods 19.
Music video for Max Cooper's Ascent
My 5-dimensional animation sets the visual stage for Max Cooper's Ascent from the album Unspoken Words. I have previously collaborated with Max on telling a story about infinity for his Yearning for the Infinite album.
I provide a walkthrough the video, describe the animation system I created to generate the frames, and show you all the keyframes
The video recently premiered on YouTube.
Renders of the full scene are available as NFTs.
Gene Cultures exhibit — art at the MIT Museum
I am more than my genome and my genome is more than me.
The MIT Museum reopened at its new location on 2nd October 2022. The new Gene Cultures exhibit featured my visualization of the human genome, which walks through the size and organization of the genome and some of the important structures.
