Just saw a program on PBS, very interesting. Apparently the universe is, and the earliest life on earth was fractal. However because of its apparent inability to change (evolve) it was replaced by a more complex dual helix mechanism.
question: are fractals important to science and specifically life?
I think the expression of our genes might be fractal in nature in many cases. That would explain how we can get so much complexity out of a relatively small set of genetic instructions. Equations for fractals are very simple too (the mandelbrot set is just Zn+1 = Zn^2 + c). Certain organisms look obviously fractal. It would be silly and expensive not to have a simple fractal genetic code behind it.
Computer scientists uses fractal-like algorithms called recursive algorithms. Also, they use fractal data structures (trees). However, these are not true fractals since they are not infinite due to limited memory. I believe fractals are also used in 3D computer graphics, as well as digital image compression.
Fractal shapes are used for antennas - the shape helps them pick up a wider range of frequencies.
I think the expression of our genes might be fractal in nature in many cases. That would explain how we can get so much complexity out of a relatively small set of genetic instructions. Equations for fractals are very simple too (the mandelbrot set is just Zn+1 = Zn^2 + c). Certain organisms look obviously fractal. It would be silly and expensive not to have a simple fractal genetic code behind it.
Computer scientists uses fractal-like algorithms called recursive algorithms. Also, they use fractal data structures (trees). However, these are not true fractals since they are not infinite due to limited memory. I believe fractals are also used in 3D computer graphics, as well as digital image compression.
Fractal shapes are used for antennas - the shape helps them pick up a wider range of frequencies.
Yes saw that, most cell phones today have fractal antennas.
The elegant simplicity IMO may even be related to the very basic structure of the universe.
Binary and fractal…....hard to beat…..
I think the expression of our genes might be fractal in nature in many cases. That would explain how we can get so much complexity out of a relatively small set of genetic instructions.
Could fractal geometrics be instrumental in the apparent increasing expansion of the universe?
And could we use an inverse fractal function to reduce the complexity of universe until we reached the most basic forms?
Could fractal geometrics be instrumental in the apparent increasing expansion of the universe?
And could we use an inverse fractal function to reduce the complexity of universe until we reached the most basic forms?
Causal Dynamical Triangulation (CDT), invented by Renate Loll and her colleagues is relevant.
Armed with last century’s insights into the nature of both quantum theory and general relativity, physicists believe that probing the structure of space and time at distances far below those currently accessible by our most powerful accelerators would reveal a rich geometric fabric, where spacetime itself never stands still but instead quantum-fluctuates wildly. One of the biggest challenges of theoretical physics today is to identify the fundamental “atoms of spacetime geometry” and understand how their interactions give rise to the macroscopic spacetime we see around us and which serves as a backdrop for all known physical phenomena.
At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time.
Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set.
Fractal geometry in cosmology without the Big Bang?:
Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers’ paradox (the “dark night sky” riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.
All these point to fractal geometry as inherent in nature from the very small to the very large. Also, CDT reveals spacetime as fundamentally dynamic and it evolves. Hence, the “increasing expansion of the universe”.
How do you put pictures on here? I had a few to show too but I can figure out what to do. I can attach but not place in post.
right click on an image you like, or if your running on Apple “control-click”, which gets you to Page Source, on my computer I get the option to:
copy image information
view image information
etc.
copy that into the text and bracket it with <img> and the magic is done.
Acknowledgment goes out to DeadMonky who taught me all. . . well some , of what I know about this.
Now if only we can figure out how to resize those images, it would be very cool.
As for fractals
I believe in the woo of fractals being representative, or should I say permeating, human life and even political life.
That’s why Jesus has been so successful in that, I believe, his experience is sort of like a Mandelbrot Set, one all struggling humans can relate to because of this woo of fractals.
Politically, tell me has anyone noticed any substantive change in how politics is done over the past three thousand years? The drum beat of the rise and fall of empires is such a repetitive storyline, it’s like once you’ve dissected one you know them all.
It seems to me that all these physical examples are only superficially described by fractals. The interesting point about fractals is that they are infinitely self-similar whereas self-similarity seems to quickly break down in these examples with each magnitude of detail consideration: molecular, atomic, subatomic, zero-sum energy field (per Krauss et al).
I think I see what your saying… but does it need to be mathematically perfect… to be counted as a fractal?
Applying the method to human cells, the 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,” says Lieberman-Aiden. . . “
What? Was I not on topic? I just added a few examples on domokato’s suggestion that fractal development might be an important connection between genotype and phenotype.
I sometimes call cauliflower and broccoli ‘frustrated romanescoes’: the fractal structure of these is not as clear as in romanesco. Obviously some of the fractal extensions overlap with others and so hide the fractal structure a little. In romanesco this does not happen. So it really could be that one small mutation that is involved in the size of the growing may heavy such a heavy influence.
Here another romanesco:
With cauliflowers you sometimes can see the spiral structure a little:
I wonder if synapses grow in a fractal manner. The brain itself seems fractal to me. Kinda like a large cauliflower…
Do we think fractally? We may look at only a small part of something and be able to deduce or imagine what that something looks like or could look like, in toto.
Hummmmm…..I also wonder if the pyramid builders knew they were constructing the first man-made fractal structure. After all fractals are CDT (Dimensional Triangulation). Also used in fixing a point by triangulation (fractal?)
, of what I know about this.
I just added a few examples on domokato’s suggestion that fractal development might be an important connection between genotype and phenotype.
