`\pi` Approximation Day Art Posters
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!
getting it mostly right
Curiously, the 22/7 rational approximation of `\pi` is more accurate (to within 0.04%) than using the first three digits 3.14, which are accurate to 0.05%.
It seems that `\pi` Approximation Day is 20% more accurate (verify on Wolfram Alpha)! And therefore definitely worth celebrating. $$ \frac{(\pi-3.14)-(22/7-\pi)}{\pi-3.14} = 0.206 $$
art of `\pi` rational approximation
The poster shows the accuracy of 10,000 rational approximations of `\pi` for each `m/n` and `m=1...10000`. Read about the details of the method.
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art of `\pi`-approximate packing
These posters show warped circles, which embody the 22/7 approximation of `\pi`, using a retro 1970's color scheme. Read about the details of the method.
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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.
Annals of Oncology cover
My cover design on the 1 September 2022 Annals of Oncology issue shows 570 individual cases of difficult-to-treat cancers. Each case shows the number and type of actionable genomic alterations that were detected and the length of therapies that resulted from the analysis.
Pleasance E et al. Whole-genome and transcriptome analysis enhances precision cancer treatment options (2022) Annals of Oncology 33:939–949.
Browse my gallery of cover designs.
Survival analysis—time-to-event data and censoring
Love's the only engine of survival. —L. Cohen
We begin a series on survival analysis in the context of its two key complications: skew (which calls for the use of probability distributions, such as the Weibull, that can accomodate skew) and censoring (required because we almost always fail to observe the event in question for all subjects).
We discuss right, left and interval censoring and how mishandling censoring can lead to bias and loss of sensitivity in tests that probe for differences in survival times.
Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Survival analysis—time-to-event data and censoring. Nature Methods 19:906–908.
3,117,275,501 Bases, 0 Gaps
See How Scientists Put Together the Complete Human Genome.
My graphic in Scientific American's Graphic Science section in the August 2022 issue shows the full history of the human genome assembly — from its humble shotgun beginnings to the gapless telomere-to-telomere assembly.
Read about the process and methods behind the creation of the graphic.
See all my Scientific American Graphic Science visualizations.