Are fractals simple or complicated objects? Or perhaps both? The beauty and attraction of many fractals stems from their complex and intricate form, with ever more detail becoming apparent under increasing magnification. Yet many fractals depend on a very simple rule, applied over and over again, a process called iteration.
The Mandelbrot set is perhaps the best known example. It is completely determined by the very simple formula z2 + c, where z and c code points in the plane or on a computer screen in terms of ‘complex numbers’. If, starting at 0 and repeatedly applying the formula to move from one point to the next, the sequence of points stay ‘close to home’, then c belongs to the Mandelbrot set and is coloured black in the pictures. If, on the other hand, the itinerary rapidly shoots off or ‘escapes’ into the distance, then c lies outside the Mandelbrot set and is coloured according to the rate of escape.
This simple rule is very easily programmed on a computer. Yet the Mandelbrot set is an extraordinarily complex object. It has a prominent cardioid, or heart shape, surrounded by near circular buds, which in turn have smaller buds attached to them. On closer inspection, stars, spirals and sea horses become apparent. Joined to these are many fine hairs on which lie miniature copies of the Mandelbrot set itself, and increased magnification reveals an endless gallery of ever more exotic features.
For its appearance alone, the Mandelbrot set would merely be a fascinating curiosity. But in recent years its remarkable mathematical properties have become enormously significant. Naturally associated with each point c of the Mandelbrot set is another fractal, called a Julia set. If c is in the main cardioid, then the Julia set is a closed loop, if c is in the largest bud, then it is formed by infinitely many loops, meeting systematically in pairs, and so on. Moreover, the Mandelbrot set is ‘universal’ in that it codes the behaviour of iteration by many formulae other than just z2 + c.
Galaxies like colorful pieces of candy fill the Hubble Ultra Deep Field 2014. The dimmest galaxies are more than 10 billion times fainter than stars visible to the unaided eye and represent the Universe in the extreme past, a few 100 million years after the Big Bang. The image itself was made with the significant addition of ultraviolet data to the Hubble Ultra Deep Field, an update of Hubble’s famous most distant gaze toward the southern constellation of Fornax. It now covers the entire range of wavelengths available to Hubble’s cameras, from ultraviolet through visible to near-infrared. Ultraviolet data adds the crucial capability of studying star formation in the Hubble Ultra Deep Field galaxies between 5 and 10 billion light-years distant.
Image Credit: NASA, ESA, H.Teplitz and M.Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst(ASU), Z. Levay (STScI)
… the two processes, that of science and that of art, are not very different. Both science and art form in the course of the centuries a human language by which we can speak about the more remote parts of reality …
One of the strongest motives that lead men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one’s own ever-shifting desires. A finely tempered nature longs to escape from the personal life into the world of objective perception and thought.
Jupiter’s Great Red Spot from Voyager 1 Color Inverted
What will become of Jupiter’s Great Red Spot? Recorded as shrinking since the 1930s, the rate of the Great Red Spot’s size appears to have accelerated just in the past few years. A hurricane larger than Earth, the Great Red Spot has been raging at least as long as telescopes could see it. Like most astronomical phenomena, the Great Red Spot was neither predicted nor immediately understood after its discovery. Although small eddies that feed into the storm system seem to play a role, a more full understanding of the gigantic storm cloud remains a topic of continued research, and may result in a better understanding of weather here on Earth. The above image is a digital enhancement of an image of Jupiter taken in 1979 by the Voyager 1 spacecraft as it zoomed by the Solar System’s largest planet. NASA’s Juno spacecraft is currently heading toward Jupiter and will arrive in 2016.
Image Credit: NASA, JPL; Digital processing: Björn Jónsson (IAAA), Color: thedemon-hauntedworld
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.