Tree of Life Diagrams

In previous blogs about Ernst Haeckel I pointed to his amazing drawings of animals and sea creatures. He also published the evolutionary tree, below, showing how humans and animals evolved from single-celled creatures.

Haeckel's diagram was published in 1879, forty-two years after Charles Darwin wrote "I think" above his sketch, probably the first diagram of it's kind.

With DNA sequencing we now have this amazing diagram of the evolutionary tree. See the University of Texas source and a New York Times article.

Mac users can download a 3-D version of the diagram by M. J. Sanderson here: http://loco.biosci.arizona.edu/paloverde/paloverde.html

More on the tree of life here: http://tolweb.org/tree/phylogeny.html

References
Zimmer, Carl (2009). "Crunching the Data for the Tree of Life", The New York Times online, Feb. 9, 2009.
http://www.nytimes.com/2009/02/10/science/10tree.html?_r=1&pagewanted=1

Wikipedia contributors, "Kunstformen der Natur" Wikipedia, The Free Encyclopedia, http://commons.wikimedia.org/wiki/Kunstformen_der_Natur (accessed February 11, 2009).

Wikipedia contributors, "Charles Darwin", Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Charles_Darwin&oldid=269994913 (accessed February 11, 2009).

David M. Hillis, Derrick Zwickl, and Robin Gutell, University of Texas. "Download Graphic Images from the Hillis/Bull Lab, Tree of Life Poster and Other Graphic Images", http://www.zo.utexas.edu/faculty/antisense/DownloadfilesToL.html (accessed February 11, 2009).

Alicia Boole Stott

Alicia Boole Stott, 1860-1940, was born in Cork, Ireland. Although she never studied mathematics she was able to visualize geometric forms in hyperbolic space. She is remembered for finding all three dimensional sections of the four dimensional polytopes and for discovering many of the semi-regular polytopes. She coined the term "polytope" to refer to a convex solid in four dimensions. She built beautiful models of polytopes.

"Perpendicular sections of the 600-Cell. Section number 7." Alicia Boole Stott
The University of Groningen, Netherlands
http://www.math.rug.nl/models/Alicia.html

References

Riddle, Larry (LRiddle@AgnesScott.edu). "Biographies of Women Mathematicians, Alicia Boole Stott". Agnes Scott College, Atlanta, Georgia.
http://www.agnesscott.edu/Lriddle/WOMEN/women.htm.

Photo Credit

Blanco, Irene Polo and van der Zalm, Lotte. "Mathematical models of surfaces, Alicia Boole Stott, 600(P), nr. 7". University of Groningen.
http://www.math.rug.nl/models/

Google Earth Oceans

Two recent software releases have huge potential for influencing art based on nature and technology. The new release of Google Earth and Adobe's Creative Suite family with Flash CS4 will tempt artists open to the concepts and imagery of science. Google Earth gives us the ability to see the ocean scape, and Flash CS4 includes basic 3D object manipulation capabilities. Web designers and developers have increasingly influenced artists, opening their eyes to all sorts of possibilities. Designers and developers working with technologists are changing the way we access science like never before. The new release of Google Earth reveals huge, amazing geological patterns in the ocean scape. The animation, data visualization, and interactive graphics capabilities of software like but not exclusive to Flash are giving scientists powerful ways to communicate ideas to the rest of us. (Also see Processing, and Rhino.)

In "Art and Nature", Arcy Douglass (writing for PORT – www.portlandart.net) brought us up to date on how artists have used natural processes and math to influence their work. A few artists have been interested in and able to absorb what science and technology have to teach. Now, science becomes more accessible, through the efforts of huge undertakings like Google, and because on a small scale thousands of technical artists and designers are working with scientists and mathematicians to improve our visualization of natural processes. Our exposure doesn't stop with our last science or math class in school. Science journals and graduate level books aren't required to tap into a lot of the amazing work going on.

Sylvia Earle said to Google, “You’ve done a great job with the dirt. But what about the water?” (See http://www.nytimes.com/2009/02/03/science/earth/03oceans.html.) The February issue of Scientific American has an excellent article explaining the origin of continuous undersea "ridges that wind around the globe like seams on a baseball." See "The Origin of the Land Under the Sea", by Peter B. Kelemen.

From Google Earth. The Pacific Ocean floor, off the coast of Maui.

From Google Earth. The Pacific Ocean floor, off the coast of southeast Mexico.

This gratuitous image from my Squared Spiral series has nothing to do with the ocean scape, but it was built in Flash Actionscript, and is influenced by the math concept of tessellation or tiling of the plane.

Squared Spiral

From a new series. Not quite as interesting as the Ulam spiral.

I've been intending to consolidate a list of Portland, Oregon artists that use some math in their work, and artists with a technical background. These are not geek artists. They are primarily interested in art and may be more or less inspired by math or technology.

I include Michael Knutson (paintings based on quasiregular rhombic tiling), Arcy Douglas (Sierpinski triangle fractals built with hexagonal tiles), Eva Lake (for her interest in the Richter Scale), and Julian Voss-Andreae (sculpture based on molecular structure, etc.). Also Stephan Soihl, and Martha Morgan (for "The Golden Ratio in Tryon Creek State Park"). More to come.

Earthquakes

A sinusoidal ridge from Sinusoidal Grids. Earthquakes happen. A noticeable rise or fall in the normal depth of coastal waters is nature's tsunami warning. Move away from the shore immediately. (See the U.S. Geological Survey Earthquake Hazards Program).

I've been trying to create a geometric representation of a landscape (mountain ridges) from a long distance, like a Google Earth image. Since I used a sinusoidal motif this reminded me of seismograph prints. So I'm combining a landscape with a seismograph-like motif.

Dart-Rhombus Recede

This is a 3-fold, dart-rhombus, radial tiling. Each dart is decorated or marked by rhombi which recede from the adjacent rhombus. This divides each dart-rhombus into ever smaller copies. Each adjacent dart-rhombus is a trivially simple fractal.


I generated this image with six rows, but I have also done a 3 row version, both of which can be seen in my Tilings project. A description of the process for generating the basic dart-rhombus structure without the decoration is here.

In these digitial drawings I superimpose an image on each tile. Sometimes the image is programmatically varied from tile to tile. In these cases the tile with its marking is no longer a true tiling in the mathematical sense, though the underlying structure is. The marking or decoration of the tiles, other than by systematic coloring, often obscures the structure. Infinitely many interesting tilings are possible without this obfuscation. I choose this approach because I'm less interested in the math than I am in inventing a quasi natural image.

Pascal Cotte and Mona Lisa at OMSI

Yesterday I was able to attend a presentation at OMSI (Oregon Museum of Science and Industry) by Pascal Cotte. OMSI is opening an exhibit on Leonardo da Vinci, featuring a whole room devoted to Cotte's 240-megapixel, multi-spectral scans of the Mona Lisa. Cotte not only invented the camera which uses 13 wavelengths from ultraviolet light to infrared; he also supervised the exhaustive analysis of the resulting images.


Through this analysis Cotte is able to reveal hidden details of how da Vinci painted the Mona Lisa, and how she appeared to da Vinci's contemporaries. The exhibit highlights Cotte's discovery of 25 secrets about the Mona Lisa, including evidence that she did in fact have eyebrows.