the path

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the path

Mandelbrot Zoom

Music:

“Let Go” - Bearcubs

“Our Demons” - The Glitch Mob & Aja Volkman (filous remix)

“Fears” - Mtns

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?

page 286 panel a - flower flower flower power. What is the power of flowers? Is it seeds?

* Giuseppe Peano*, born on 27th August 1858, was an Italian mathematician. The author of over 200 books and papers, he was a founder of

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 ^_^

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.

structure of chaos

Regenaissance (Polyversikube)

Michael Carini | Acrylic on Canvas | 144” x 144” | 2013

**9 Canvases…95, 126, 814, 720 Possible Orientations**

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!

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 2·3^{n }more circles on the *n ^{th }*level of the gasket, for a total of 3

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!

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.

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.

Fractal Cosmology theory THE ITERATION Collection by Lisa Shahno

SOURCE:

I LOVE MATHEMATICS form Curiosamathematica.tumblr.com

**Curiosa Mathematica:**

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?