Chaotic dinosaurs?

In the comic above, XKCD is objecting to Jurassic Park (21 years after the movie was released):

MALCOLM: You see? The tyrannosaur doesn’t obey set patterns or park schedules. The essence of Chaos.

ELLIE: I’m still not clear on Chaos.

MALCOLM: It simply deals with unpredictability in complex systems. The shorthand is the Butterfly Effect. A butterfly can flap its wings in Peking and in Central Park you get rain instead of sunshine.

No, Ian Malcolm, XKCD is right. That doesn’t really clear things up. And I’m pretty sure that topological mixing is actually more fundamental to the concept of Chaos:

Wired also has a piece on the anniversary of the film (concentrating on the special effects).

Arabidopsis thaliana: a model plant

Arabidopsis thaliana, the thale cress (photo above by Peggy Greb, picture below by Johann Georg Sturm and Jacob Sturm, 1796) is a small flowering plant in the family Brassicaceae – the mustard/cabbage family.

During much of the 20th century, A. thaliana was the target of extensive research, facilitated by the small size of the plant (and of its genome), its short life cycle, and its suitability for light microscopy. Sequencing of the genome was completed in the year 2000, and the genome is available at arabidopsis.org. The open-access peer-reviewed The Arabidopsis Book also collates information on the plant, which is in many ways the botanical equivalent of Caenorhabditis elegans. It has taught the world a great deal.

The Google Ngram below shows the explosion in Arabidopsis-related literature since about 1990, outstripping even work on C. elegans:

The analemma

If you photograph the sun at the same time every day (or every few days), you will find that the sun traces out a path in the sky, called the analemma. György Soponyai, in Budapest (Hungary), did exactly that at 8 AM each morning between 29 January last year and 6 January this year, to produce the wonderful photograph below (click to zoom):

More analemma photographs (by Anthony Ayiomamitis) can be found here. The shape of the analemma results from the fact that (1) the Earth is tilted on its axis by 23.5° and (2) the Earth orbits the sun in an ellipse, rather than a circle. The diagram below shows the calculated analemma for 12 noon at the Royal Observatory, Greenwich (latitude 51.48° N):

The concept of the analemma can also be used in constructing sundials. If an appropriate analemma is placed in the centre of the sundial, a gnomon placed at the right point on the analemma will correctly tell the time with its shadow (except for daylight-saving, of course).

Such sundials are popular in parks, because the viewer can stand on the analemma at a position corresponding to the current date, and his or her shadow will tell the time, without the need for additional time-of-year correction. I photographed the sundial above and below at Mt Stromlo Observatory in June 2012. It can be seen that the time was about 2:20 PM.

Fire rainbows!

Fire rainbows, illustrated in the photo by “Dehk” above, are actually not rainbows at all, but a halo phenomenon related to the sun dogs previously discussed.

Fire rainbows (or, more accurately, fragments of circumhorizontal arcs) are formed at an angle of 46° from the Sun, and result from light refracting through ice crystals in high-altitude cirrus clouds. In particular, they result from light refracting through one of the 90° angles of an ice crystal, like so:

Fire rainbows are on my bucket list too, given the many beautiful pictures of the phenomenon on Flickr and on Wikimedia Commons.

Looking at Pluto

In what they are calling a “preanniversary,” Wired is highlighting the image above (thanks to NASA, ESA, H. Weaver, A. Stern, and the HST Pluto Companion Search Team) of everybody’s favourite dwarf planet. A year from now, New Horizons will be giving us much better pictures of Pluto. And we will finally find out if Robert Silverberg was right.

ISEE-3 runs dry

The ISEE-3 Reboot Project started well, but it now seems that this antique spacecraft is out of gas. Not out of fuel, per se, but out of the nitrogen needed to pressurise the fuel.

As at July 11, communication with the spacecraft had a 29.159 second round-trip time. Since the speed of light is 299,792,458 metres per second, this corresponds to a distance of 4,370,821 kilometres (eleven times the average distance to the moon). ISEE-3 will fly around the moon in August (hopefully not into the moon), and then orbit the sun. The ISEE-3 Reboot team will continue to receive data from the spacecraft (and perhaps do some science), but the original plans will have to be abandoned. Which is a great pity.

Update 1: the ISEE-3 Reboot team have not yet given up, and are attempting some “deep space plumbing repairs.” It seems that lack of gas may not be the problem, and that the situation is both more complicated and more hopeful.

Update 2: it does seem that lack of nitrogen is the problem after all. This means that trajectory can no longer be controlled, but plans are nevertheless to put ISEE-3 into “citizen science” mode.

Sun dogs!

Sun dogs, illustrated above, are an atmospheric phenomenon resulting from tiny ice crystals in the air. In fact, they are part of a halo or parhelion around the Sun (or Moon), at an angle of 22° from it. This halo is typically intensified to the left and right of the Sun, forming the two “dogs” (and sometimes also intensified above and below). An explanation must therefore come in two parts – why the halo, and why the intensification?

For the first question, the tiny ice crystals floating in the air over wintry landscapes act as tiny prisms, deflecting the light by about 22° (see the diagram below, superimposed on a microscope image of an Antarctic ice crystal, by Hannes Grobe):

Because prisms deflect different colours slightly differently (as shown below), a slight rainbow effect is sometimes visible in the 22° halo, with red on the inside. However, because the deflection actually occurs over a range of angles from 22° upwards (depending on the orientation of the crystals), the blue and green colours are usually completely washed out.

The second question was: why the intensification on the two sides of the sun? This occurs because flat ice crystals have a tendency to fall through the air like paper plates, with the hexagonal surfaces at the top and bottom. Intensification above and below the sun is sometimes also seen, forming a kind of cross. This results from other, rod-shaped, ice crystals which are oriented with their long axis horizontal.

The diagram below shows the two kinds of ice crystal:

I have not been fortunate enough to see sun dogs myself, but it’s on the bucket list.