Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
Poetry is just the evidence of life. If your life is burning well, poetry is just the ashLeonard Cohenwatch

filling space: fun


Visualization Tour, Melbourne, October 9–20, 2014


visualization + design

Like paths? Got your lines twisted in a bunch?
Take a look at my 2014 Pi Day art that folds Pi.

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca

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.

All the art here is available for purchase at Fine Art America.

Here are some samples of the posters. They are classified into categories.


news + thoughts

Nested Designs—Assessing Sources of Noise

Mon 29-09-2014

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Nested designs. (read)

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.

...more about the Points of Significance column

Replication—Quality over Quantity

Tue 02-09-2014

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Replication. (read)

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.

...more about the Points of Significance column

Monkeys on a Hilbert Curve—Scientific American Graphic

Tue 19-08-2014

I was commissioned by Scientific American to create an information graphic that showed how our genomes are more similar to those of the chimp and bonobo than to the gorilla.

I had about 5 x 5 inches of print space to work with. For 4 genomes? No problem. Bring out the Hilbert curve!

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Our genomes are much more similar to the chimp and bonobo than to the gorilla. And, we're practically still Denisovans. (details)

To accompany the piece, I will be posting to the Scientific American blog about the process of creating the figure. And to emphasize that the genome is not a blueprint!

As part of this project, I created some Hilbert curve art pieces. And while exploring, found thousands of Hilbertonians!

Happy Pi Approximation Day— π, roughly speaking 10,000 times

Wed 13-08-2014

Celebrate Pi Approximation Day (July 22nd) with the art of arm waving. This year I take the first 10,000 most accurate approximations (m/n, m=1..10,000) and look at their accuracy.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Accuracy of the first 10,000 m/n approximations of Pi. (details)

I turned to the spiral again after applying it to stack stacked ring plots of frequency distributions in Pi for the 2014 Pi Day.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Frequency distribution of digits of Pi in groups of 4 up to digit 4,988. (details)

Analysis of Variance (ANOVA) and Blocking—Accounting for Variability in Multi-factor Experiments

Mon 07-07-2014

Our 10th Points of Significance column! Continuing with our previous discussion about comparative experiments, we introduce ANOVA and blocking. Although this column appears to introduce two new concepts (ANOVA and blocking), you've seen both before, though under a different guise.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Analysis of variance (ANOVA) and blocking. (read)

If you know the t-test you've already applied analysis of variance (ANOVA), though you probably didn't realize it. In ANOVA we ask whether the variation within our samples is compatible with the variation between our samples (sample means). If the samples don't all have the same mean then we expect the latter to be larger. The ANOVA test statistic (F) assigns significance to the ratio of these two quantities. When we only have two-samples and apply the t-test, t2 = F.

ANOVA naturally incorporates and partitions sources of variation—the effects of variables on the system are determined based on the amount of variation they contribute to the total variation in the data. If this contribution is large, we say that the variation can be "explained" by the variable and infer an effect.

We discuss how data collection can be organized using a randomized complete block design to account for sources of uncertainty in the experiment. This process is called blocking because we are blocking the variation from a known source of uncertainty from interfering with our measurements. You've already seen blocking in the paired t-test example, in which the subject (or experimental unit) was the block.

We've worked hard to bring you 20 pages of statistics primers (though it feels more like 200!). The column is taking a month off in August, as we shrink our error bars.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of Variance (ANOVA) and Blocking Nature Methods 11:699-700.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

...more about the Points of Significance column

Designing Experiments—Coping with Biological and Experimental Variation

Thu 29-05-2014

This month, Points of Significance begins a series of articles about experimental design. We start by returning to the two-sample and paired t-tests for a discussion of biological and experimental variability.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Designing Comparative Experiments. (read)

We introduce the concept of blocking using the paired t-test as an example and show how biological and experimental variability can be related using the correlation coefficient, ρ, and how its value imapacts the relative performance of the paired and two-sample t-tests.

We also emphasize that when reporting data analyzed with the paired t-test, differences in sample means (and their associated 95% CI error bars) should be shown—not the original samples—because the correlation in the samples (and its benefits) cannot be gleaned directly from the sample data.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.