Fractal Geometry is based on the idea of scale invariance which means that a figure is the same, or is invariant, no matter on what scale it is observed. In other words, the figure is constructed by repeating the same pattern at smaller and smaller scales. The fern is certainly one of the best examples for understanding this idea: a small part of the figure when enlarged reproduces the original figure (or if you will, the part contains the whole). An object which possesses this property is called a fractal. From a mathematical point of view, the repetition of patterns at smaller and smaller scales can be continued to infinity. In the real word, nevertheless, the repetition stops after a certain number of jumps.
A fractal construction is extremely interesting for reasons of effectiveness. For example, if one wants to insert the largest sheet possible in the smallest possible volume, by folding it up in such a way that its faces never touch, one must give it a fractal shape. In addition, the instructions for such a folding are very simple (and can be written in very few words) since it suffices to state that the same folding pattern is repeated many times in succession. This is surely why one finds many fractal objects in nature: the instructions for their growth can be encoded in very little space in DNA.
This auto-repetition of the same structure can also be applied to phenomena which vary in time. For example, the fluctuations of the stock market possess a statistical fractal structure, that is to say, the fluctuations over a year are similar on the average to those over a month, or to those over a day, or even to those over an hour. To put it another way, if one “enlarges” the fluctuations over one day, one obtains fluctuations which could very well be those over a year. Note, however, this is not always true.
Let’s take for example the saw : if one selects a small portion of the blade of the saw (a tooth) and then enlarge it, one does not obtain a new saw at all but only a very big tooth! In other words, on theblade of a saw, there are not teeth on teeth on teeth, etc.
Even if in certain cases the scale invariance is only statistical (stock market fluctuations, coastlines, clouds), it is nevertheless rigorously defined with what is called the fractal dimension, which measures in a way the degree of “roughness” of the fluctuations or of the boundaries of the object.
Researchers have discovered how the DNA is packed into our cells in such a way that the roughly 2 meters of DNA in each cell doesn’t tangle, and is easily accessible when it’s needed to make proteins. And the key is: Fractal Geometry!
‘…Researchers found that the genome has a highly organized structure. Small pieces of DNA fold into globs, and those globs fold into larger globs and so on. The researchers report that this “globule of globules of globules” is fractal, meaning it is organized in such a way that it has the same pattern no matter how far you zoom in. This fractal shape is “super-dense, but has no knots,”
The DNA of a Eukaryotic chromosome is shaped as a fractal helix. The fractal shape allows for all sizes of the chromosome to be unpacked and transcribed efficiently, from individual genes to long sections of DNA with thousands of co-dependent genes and regulatory sequences.
During DNA replication, both strands of the double helix act as templates for the formation of new DNA molecules. Copying occurs at a localized region called the replication fork, which is a Y-shaped structure where new DNA strands are synthesized by a multi-enzyme complex. Here, the DNA to be copied enters the complex from the left. One new strand is leaving at the top of frame and the other new strand is leaving at bottom.
The first step in DNA replication is the separation of the two strands by an enzyme called helicase. This spins the incoming DNA to unravel it: at 10,000 RPM in the case of bacterial systems. The separated strands are called three prime (3’) and five prime (5’), distinguished by the direction in which their component nucleotides join up. The 3’ DNA strand, also known as the leading strand, is diverted to a DNA polymerase and is used as a continuous template for the synthesis of the first daughter DNA helix. The other half of the DNA double helix, known as the lagging strand, has the opposite 3’-to-5’ orientation and consequently requires a more complicated copying mechanism. As it emerges from the helicase, the lagging strand is organized into sections called Okazaki fragments. These are then presented to a second DNA polymerase enzyme in the preferred 5’-to-3’ orientation. These sections are then effectively synthesized backwards. When the copying is complete, the finished section is released and the next loop is drawn back for replication.
Intricate as this mechanism appears, numerous components have been deliberately left out to avoid complete confusion. The exposed strands of single DNA are covered by protective binding proteins. And in some systems, multiple Okazaki fragments may be present. The molecular reality is very different from the iconic image of the double helix neatly separating into two DNA copies as so often depicted.
Developed by the DNA Learning Center at Cold Spring Harbor Laboratory in Cold Spring Harbor, New York, USA.
Recognize that the very molecules that make up your body, the atoms that construct the molecules, are traceable to the crucibles that were once the centers of high mass stars that exploded their chemically rich guts into the galaxy, enriching pristine gas clouds with the chemistry of life. So that we are all connected to each other biologically, to the earth chemically and to the rest of the universe atomically. That’s kinda cool! That makes me smile and I actually feel quite large at the end of that. It’s not that we are better than the universe, we are part of the universe. We are in the universe and the universe is in us.
This large solar flare, produced by an active region of the sun (AR9077), triggered magnetic storms and knocked out satellites when it created a solar storm on July 14, 2000. Nicknamed the Bastille Day Event, it was the third largest storm of its kind in the past 30 years, and the biggest solar radiation event since 1989. The Slinky-like loops represent magnetic field lines.
The orbiting Transition Region and Coronal Explorer (TRACE) satellite captured this close-up image after the flare erupted. Recorded in extreme ultraviolet light, it covers a 230,000-by-77,000 kilometer area on the sun’s surface and shows a one-million-degree solar plasma cooling down.
Here is one of the sharper views of the Sun ever taken. This stunning image shows remarkable details of a dark sunspot across the image bottom and numerous boiling granules which appear like kernels of corn across the top. Taken in 2002, the picture was made using the Swedish Solar Telescope operating on the Canary Island of La Palma.
The universe is probably littered with the one-planet graves of cultures which made the sensible economic decision that there’s no good reason to go into space—each discovered, studied, and remembered by the ones who made the irrational decision.