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visualization + design
2013 Pi Day Art Posters — March 14
download
numbers.tgz
1,000,000 digits of π, φ, e and ASN.
watch video
Watch the video at Numberphile about my art.
2014 Pi Day art
Explore Pi Day art for 2014.
buy artwork
All the artwork can be purchased from Fine Art America.
transcend, don't repeat, yourself
Proclus got it right when he said (as quoted by M. Kline in Mathematical Thought from Ancient to Modern Times)
Wherever there is number, there is beauty.
So let's explore what Pi looks like with something whimsical and pretty and colourful. Rational art of the highly irrational, a regime where beauty runs with her hair down and lets her "ribbons to flow confusedly." Robert Herrick says it well in Sweet Disorder,
I see a wild civility;—
Do more bewitch me, than when art
Is too precise in every part.
The posters explore the relationship between adjacent digits in Pi, which are encoded by color using the scheme shown above. The design appears to shimmer due to the luminance effect. In some versions of the poster, adjacent identical (or similar) digits are connected by lines.
The recipe for each poster is included and gives the color of the ith outer/inner circle. π[i] is used to represent the ith digit of π. For example, the recipe
π[i] / π[i+1]
generates a poster whose outer circle color encodes the ith digit and the inner circle color encodes the next digit (i+1). In this scheme, inner and outer circles of adjacent positions have the same color.
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source and methods
The posters were generated automatically with a Perl script that generated SVG files. Post processing and layout was done in Illustrator. If you are interested in depicting your favourite number this way, let me know.
The design was inspired by the beautiful AIDS posters by Elena Miska.
love in Pi—you can find it here
I calculated Pi to 13,099,586 digits and then I found love.
It's fun to look for words in Pi. I wanted to know the first time that love appears in Pi. When encoded using the scheme a=0, b=1, ..., z=25, love is the digit 1114214. This digit appears first at position 13,099,586 (...892199163111142148187311392...). And, of course, infinitely many times after that.
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If you use the scheme a=1, b=2, ..., z=26, then love becomes 1215225. This is first seen at 6,317,696 (...610311912912152256606850141...).
Because the digits of Pi never repeat and are distributed randomly (as far as we know), if you look long enough you'll find all the words in Pi infinitely many times.
700 digits (20 x 35)
π[i] / grey, 80% opacity
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π[i] / π[i+1], 80% opacity
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2,800 (40 x 70) digits
π[i] / grey, 80% opacity (equal neighbours connected)
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π[i] / π[i+1], 80% opacity (equal neighbours connected)
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— / π[i+1] (equal neighbours connected, unconnected digits not shown)
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π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0,1,2}, unconnected digits not shown)
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π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0..5}, unconnected digits not shown)
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Pi (π): — / red (equal neighbours connected, unconnected digits not shown)
Phi (φ): — / white (equal neighbours connected, unconnected digits not shown)
e: — / grey (equal neighbours connected, unconnected digits not shown)
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11,400 (80 x 140) digits
π[i] / grey, 80% opacity (equal neighbours connected)
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π[i] / π[i+1], 80% opacity (equal neighbours connected)
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π[i] / π[i+1] &>
π[i] / grey, 80% opacity (equal neighbours connected, unconnected digits not shown)
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π[i] / π[i+1], 80% opacity (equal neighbours connected, unconnected digits not shown)
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news + thoughts
Points of Significance Column Now Open Access
Nature Methods has announced the launch of a new statistics collection for biologists.
As part of that collection, announced that the entire Points of Significance collection is now open access.
This is great news for educators—the column can now be freely distributed in classrooms.
Before and After—Designing Tiny Figures for Nature Methods
I've posted a writeup about the design and redesign process behind the figures in our Nature Methods Points of Significance column.
I have selected several figures from our past columns and show how they evolved from their draft to published versions.
Clarity, concision and space constraints—we have only 3.4" of horizontal space— all have to be balanced for a figure to be effective.
It's nearly impossible to find case studies of scientific articles (or figures) through the editing and review process. Nobody wants to show their drafts. With this writeup I hope to add to this space and encourage others to reveal their process. Students love this. See whether you agree with my decisions!
Sources of Variation
Past columns have described experimental designs that mitigate the effect of variation: random assignment, blocking and replication.
The goal of these designs is to observe a reproducible effect that can be due only to the treatment, avoiding confounding and bias. Simultaneously, to sample enough variability to estimate how much we expect the effect to differ if the measurements are repeated with similar but not identical samples (replicates).
We need to distinguish between sources of variation that are nuisance factors in our goal to measure mean biological effects from those that are required to assess how much effects vary in the population.
Altman, N. & Krzywinski, M. (2014) Points of Significance: Two Factor Designs Nature Methods 11:5-6.
Background reading
1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.
2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.
3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.
Two Factor Designs
We've previously written about how to analyze the impact of one variable in our ANOVA column. Complex biological systems are rarely so obliging—multiple experimental factors interact and producing effects.
ANOVA is a natural way to analyze multiple factors. It can incorporate the possibility that the factors interact—the effect of one factor depends on the level of another factor. For example, the potency of a drug may depend on the subject's diet.
We can increase the power of the analysis by allowing for interaction, as well as by blocking.
Krzywinski, M., Altman, (2014) Points of Significance: Two Factor Designs Nature Methods 11:1187-1188.
Background reading
Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.
Nested Designs—Assessing Sources of Noise
Sources of noise in experiments can be mitigated and assessed by nested designs. This kind of experimental design naturally models replication, which was the topic of last month's column.
Nested designs are appropriate when we want to use the data derived from experimental subjects to make general statements about populations. In this case, the subjects are random factors in the experiment, in contrast to fixed factors, such as we've seen previously.
In ANOVA analysis, random factors provide information about the amount of noise contributed by each factor. This is different from inferences made about fixed factors, which typically deal with a change in mean. Using the F-test, we can determine whether each layer of replication (e.g. animal, tissue, cell) contributes additional variation to the overall measurement.
Krzywinski, M., Altman, N. & Blainey, P. (2014) Points of Significance: Nested designs Nature Methods 11:977-978.
Background reading
Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.
Replication—Quality over Quantity
It's fitting that the column published just before Labor day weekend is all about how to best allocate labor.
Replication is used to decrease the impact of variability from parts of the experiment that contribute noise. For example, we might measure data from more than one mouse to attempt to generalize over all mice.
It's important to distinguish technical replicates, which attempt to capture the noise in our measuring apparatus, from biological replicates, which capture biological variation. The former give us no information about biological variation and cannot be used to directly make biological inferences. To do so is to commit pseudoreplication. Technical replicates are useful to reduce the noise so that we have a better chance to detect a biologically meaningful signal.
Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.
Background reading
Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.
Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.