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Mandelbrot Set Zoom
Tue, 2009-06-02 00:48
#1
Spectrum
Mandelbrot Set Zoom
Tue, 2009-06-02 01:00
#2
Spectrum
This is where the "pretty pictures" part starts to happen. If you zoom in on a circle this way, you wouldn't see anything interesting; the edge of the circle would simply look like a straight line after a while. Zooming into a fractal like the Mandelbrot Set, though, is much more interesting. In fact, if you keep zooming in to any point on its boundary, the border will never smooth out; there will always be finer and finer details as you keep zooming in.
One problem with making really deep zooms, though, is that it takes a lot of computer time. At higher magnifications, the computer has to be more and more precise in the math it does (just like you have to be more precise when balancing a checkbook with five digits in the numbers than if there are only two or three). Also, at the higher magnifications, it usually takes more repetitions to see how each point behaves. Finally, there is a limit to the precision of arithmetic that any computer can do easily (the computer equivalent of "in its head". The computer can do more precise math than this, but it's a long, complicated process. The result of all these is that larger zooms take a really really long time.
The next time, I'll explain specifically how to write a simple computer program to draw the Mandelbrot Set. (If you understand complex numbers and programming and want the gory details, the Mandelbrot Set is located within two units of the origin; the equation to run is Z <-- Z^2 + C (where Z starts out as 0+0i and C is the complex coordinate of the point in question.) Run this until |Z| > 2.0 or you reach an iteration limit (try 100 for starters, then see if 1000 looks any better.)The Mandelbrot Set
Tue, 2009-06-02 11:12
#3
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Some people would like to think if we but tap a new process "for robotic cultures" we might be able to make the most perfect society? So perspective is put in reductionist modes and all the things that make thinking irrational, become the idea that the deeper you go, the more irrational a neuron connect can be. What if under a under a guiding principal? A Pheromone? Bee's do it?
See:When It Comes to Photosynthesis, Plants Perform Quantum Computation
Plants soak up some of the 1017 joules of solar energy that bathe Earth each second, harvesting as much as 95 percent of it from the light they absorb. The transformation of sunlight into carbohydrates takes place in one million billionths of a second, preventing much of that energy from dissipating as heat. But exactly how plants manage this nearly instantaneous trick has remained elusive. Now biophysicists at the University of California, Berkeley, have shown that plants use the basic principle of quantum computing—the exploration of a multiplicity of different answers at the same time—to achieve near-perfect efficiency.
Biophysicist Gregory Engel and his colleagues cooled a green sulfur bacterium—Chlorobium tepidum, one of the oldest photosynthesizers on the planet—to 77 kelvins [–321 degrees Fahrenheit] and then pulsed it with extremely short bursts of laser light. By manipulating these pulses, the researchers could track the flow of energy through the bacterium's photosynthetic system. "We always thought of it as hopping through the system, the same way that you or I might run through a maze of bushes," Engel explains. "But, instead of coming to an intersection and going left or right, it can actually go in both directions at once and explore many different paths most efficiently."
In other words, plants are employing the basic principles of quantum mechanics to transfer energy from chromophore (photosynthetic molecule) to chromophore until it reaches the so-called reaction center where photosynthesis, as it is classically defined, takes place. The particles of energy are behaving like waves. "We see very strong evidence for a wavelike motion of energy through these photosynthetic complexes," Engel says. The results appear in the current issue of Nature.
QUANTUM CHLOROPHYLL: Sunlight triggers wave-like motion in green chlorophyll, embedded in a protein structure, depicted in gray here, that guides its function. GREGORY ENGEL
Employing this process allows the near-perfect efficiency of plants in harvesting energy from sunlight and is likely to be used by all of them, Engel says. It might also be copied usefully by researchers attempting to create artificial photosynthesis, such as that in photovoltaic cells for generating electricity. "This can be a much more efficient energy transfer than a classical hopping one," Engel says. "Exactly how to implement that is a very difficult question."
It also remains unclear exactly how a plant's structure permits this quantum effect to take place. "[The protein structure] of the plant has to be tuned to allow transfer among chromophores but not to allow transfers into [heat]," Engel says. "How that tuning works and how it is controlled, we don't know." Inside every spring leaf is a system capable of performing a speedy and efficient quantum computation, and therein lies the key to much of the energy on Earth.
