fractal theory

youtube

[HD] These 38 Minutes Will Blow Your Mind! (Quantum + Fractal Science)

Maybe these different fields of science that are on the brink of discovery are showing us something not so different from each other.

The Universe is connected. This discovery can bridge the separation between light and sound, which exists as one in the higher dimensions. Take these lessons and apply them to your every day life. You can guide your way through the multiverse, and everything in your life will fall into place.

The Universe is Fractal; it is infinite. Everything within it, including yourself, is also infinite. Quantum Physics is the study of this grand concept itself. I highly recommend any other quantum physicist to research the field theory, with Fractal Geometry in mind.

I ♥ mathematics

Some days ago I noticed a brilliant bumper sticker, saying “I ♥ topology” where the heart was replaced by a topologically homeomorphic disk (●). Amused by the idea, I tried to work out some related versions for other mathematical subjects. Here they are:

  • For geometry, the obvious choice was a cardioid:

  • I’m thinking of changing “Algebra” into “Arithmetic” here:

  • A connect-the-dots heart for graph theory:

  • Perhaps fractals aren’t really a mathematical subject on their own, but nevertheless they are too popular:

  • Too bad a heart shape doesn’t have that many symmetries:

  • This one is difficult categorizing! It’s related to Frobenius algebras, module and representation theory, topological quantum field theory… Which mathematical subject should it represent?

  • A knotted heart for knot theory:

  • I like this one, the Lorenz attractor for chaos theory:

  • The heart-shaped Bonne projection:

  • I hope you recognize a Venn diagram here:

  • Hmmm, statistics, a pie chart?

  • Finally, this is the one it all started with:

What do you guys think? I’m still thinking about a heart for genuine algebra, linear algebra, number theory, combinatorics and mathematical logic. Please share any remarks, ideas, subjects?

7

A few more attractors. Those are purely trigonometric.

What I find curious is the last two.

I used the follow eq:

xn=b*sin(c*x)-sin(b*y)-(abs(d+b)*sin(x));
yn=a*cos(c*x)+cos(b*y)-(abs(c+a)*cos(y));

And for some values of a,b,c,d and specific initial values it gives the structure saw at the last two images and is the one on the bifurcation diagram.

Giuseppe Peano, born on 27th August 1858, was an Italian mathematician. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation ( in his first book dealing with mathematical logic, the modern symbols for the union and intersection of sets appeared for the first time.). The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction.

Moreover, Peano’s famous space-filling curve appeared in 1890 as a counterexample. He used it to show that a continuous curve cannot always be enclosed in an arbitrarily small region. This was an early example of what came to be known as a fractal.

He has done so many things ^_^ 

Anton Stankowski

Anton Stankowski was a German graphic designer, photographer and painter. He developed an original Theory of Design and pioneered Constructive Graphic Art. Typical Stankowski designs attempt to illustrate processes or behaviours rather than objects. Such experiments resulted in the use of fractal-like structures long before their popularization. Enjoy: Pure Stankowski!

3

The Apollonian gasket is a fractal constructed from a triple of circles, where each circle is tangent to the other two. Each level continues this pattern, adding 2·3more circles on the nth level of the gasket, for a total of 3n+1 + 2 circles after n stages. Repeating this process and taking the limit gives an object like the gasket pictured above on the left.

The Apollonian gasket is also closely related to the undirected graph known as the Apollonian network. The network can be created by first taking three tangent circles, inscribing a circle in the gap created by the three circles, and continuing this process, and then giving each circle a vertex and each pair of tangent circles an edge. This process is seen in the second picture above which shows how it is related to the gasket, and the construction leads to the object pictured on the right.

Pretty interesting relation between the continuous fractal and the discrete graph!

Whether we’re gazing up through a telescope or down through a microscope, either way we’re looking at infinity unfolding in much the same patterns. This elegance and consistency seems to me rather more impressive than the petty myths of some desert-dwelling tribesmen a couple of thousand years ago.

3

Michael Carini | Regenaissance (Polyversikube) | Acrylic on Canvas 

9 Canvas Polyptych | 48" x 48" Each | 2013 

“Regenaissance (Polyversikube)” is a nine canvas polyptych conceptually inspired by the principle elements of fractals, the Golden Ratio, and a Rubik’s Cube. The name “Regenaissance” is an abstract composite derived from the words Renaissance (meaning “rebirth”) and Genesis (meaning “the beginning”). Presented in a 3 x 3 structural format, each of the nine components can be moved, rotated, and rearranged so that any side of any element can connect to any side of any of the other eight pieces. The result of the calculated configurations is a broad and almost limitless spectrum of orientations and variations with which to play; 95,126,814,720 to be exact. 

10

SOURCE:

I LOVE MATHEMATICS form Curiosamathematica.tumblr.com

Curiosa Mathematica:

I ♥ mathematics

Some days ago I noticed a brilliant bumper sticker, saying “I ♥ topology” where the heart was replaced by a topologically homeomorphic disk (●). Amused by the idea, I tried to work out some related versions for other mathematical subjects. Here they are:

  • For geometry, the obvious choice was a cardioid:

  • I’m thinking of changing “Algebra” into “Arithmetic” here:

  • A connect-the-dots heart for graph theory:

  • Perhaps fractals aren’t really a mathematical subject on their own, but nevertheless they are too popular:

  • Too bad a heart shape doesn’t have that many symmetries:

  • This one is difficult categorizing! It’s related to Frobenius algebras, module and representation theory, topological quantum field theory… Which mathematical subject should it represent?

  • A knotted heart for knot theory:

  • I like this one, the Lorenz attractor for chaos theory:

  • The heart-shaped Bonne projection:

  • I hope you recognize a Venn diagram here:

  • Hmmm, statistics, a pie chart?

  • Finally, this is the one it all started with:

What do you guys think? I’m still thinking about a heart for genuine algebra, linear algebra, number theory, combinatorics and mathematical logic. Please share any remarks, ideas, subjects?