Max Cooper - Transcendental Tree Map (Official video by Martin Krzywinski and Nick Cobby)
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Max Cooper:
For the «Yearning for the Infinite» project I looked for different ways of visualising the infinite, interspersed between imagery of humans in endless pursuit. For one chapter I wanted to visualise the digits of a transcendental number, thought to be endless and non-repeating. Martin Krzywinski specialises in visualising these digits amongst many other things, and one of my favourite images is his tree map of pi, which presents this endless nested chaos in beautiful visual form. I wanted to map that growing randomness and chaotic detailed structural form to the piece of music, so I collaborated with the great music software developer, Alexander Randon on a special tool which allows the construction of musical fractals and many other complex melodic forms. With this tool I started the piece with a simple melodic structure, which is iteratively broken down into more and more complex melodies as the tree map breaks down the initially simple first digit into more and more complex sub-structures. With the aesthetic as a whole becoming this sea of interacting notes, partly random, but with a global form emerging eventually, as the circle is embodied by the chaos of the digits of pi.
Nick Cobby collaborated with Martin to bring this idea to life in animated form for the visual show, with a hyper-detailed tree map structure growing all around the audience. And if youre interested in the ideas behind this I delved into this chapter in some detail in a recent blog essay here (which also comes as a poster with Martins tree map image inside the album vinyl package): maxcooper.net/transcendental-tree-map
Martin Krzywinski:
The transcendental tree map encodes the first 20,244 digits of Pi = 3.1415...7012.
The construction of the map begins with dividing the canvas with 3 vertical lines, which forms 4 rectangles. Each of the four rectangles formed by this process is divided with 1, 4, 1 and 5 horizontal lines, respectively. This forms 2 5 2 6 = 15 rectangles. Each of the 15 rectangles is divided by vertical lines according to the next 15 digits of Pi. This process repeats until we have performed the loop 7 times.
The division of each rectangle is not even—the positions of the lines are slightly jittered. This gives the map a more organic feel.
The number of digits encoded in each loop is 1, 4, 15, 98, 548, 2,962 and 17,180. In total, 17,180 vertical and 3,064 horizontal lines are drawn and these form the backbone of the map.
The video is created by layering numerous animations of the construction of the map, in which the rate and order of line growth is varied. Blinking rectangles indicate that the lines for a digit have completed drawing.
Original tree map and animation clips by Martin Krzywinski.
Compositing, coloring, synchronization and other post-processing by Nick Cobby.
Nick Cobby:
The challenge with Transcendental Tree Map was to bring to life Martin Krzywinskis amazing scientific visualisations of Pi. They are so dense and complex, that a considered approach was needed to ensure the computer systems could handle all the information and still maintain clarity. We had a twofold approach, using automated coded sequences from Martin and then manual digital manipulation and editing from me. Using both a generative and manual approach parallels the juxtaposition of order and randomness inherent in Martins work, and the hypnotic music Max created.
Although all Martins sequence outcomes are different, they all start with the principle rule of Pi, and when placed on top of each other, they all occupy the same grid space allowing layering and using some of the sequences as alpha channels to reveal others underneath. At any one time there are up to 30 sequences running at once. At times I wanted it to look more organic, with line tracers drawing like roots of a tree, or holes appearing in the data then glitching back to its organised structure, like its constantly battling itself. When the visual is at its peak, the construction and destruction of the order of the tree map is constant, and the notion of the infinity is revealed through the endless visual possibilities.
The transcendental tree map was originally created for 2015 Pi Day (http://mkweb.bcgsc.ca/pi/piday2015/posters.mhtml) by Martin Krzywinski (http://mkweb.bcsgc.ca) (@MKrzywinski), who has been creating Pi Day art (http://mkweb.bcgsc.ca/pi/piday.mhtml) since 2013. Martin is a staff scientist at Michael Smiths Genome Sciences Centre at BC Cancer (http://www.bcgsc.ca) where he works on data visualization.
Max Cooper
maxcooper.net/
Instagram: @maxcoopermax
Nick Cobby
nickcobby.com
Instagram: @nickcobby
Martin Krzywinski
mkweb.bcgsc.ca/
And the whole album project is explained at: www.yearningfortheinfinite.net