Sketchtwit

Deadly…

Thu, 31 May 2012 09:09:25 +0100

Deadly…

mmex: Morris Louis, Abstract Expressionist

Wed, 30 May 2012 14:20:29 +0100

mmex:

Morris Louis, Abstract Expressionist

thestrutny: Here are the first pictures from the set of All Is...

Wed, 30 May 2012 11:58:00 +0100

thestrutny:

Here are the first pictures from the set of All Is By My Side, the unauthorized Jimi Hendrix biopic starring Andre 3000. See more of the photos

Photo

Tue, 29 May 2012 18:46:54 +0100

"For the only way one can speak of nothing is to speak of it as though it were something, just as the..."

Mon, 14 May 2012 22:20:12 +0100

“For the only way one can speak of nothing is to speak of it as though it were something, just as the only way one can speak of God is to speak of him as though he were a man, which to be sure he was, in a sense, for a time, and as the only way one can speak of man, even our anthropologists have realized that, is to speak of him as though he were a termite.”

- Watt, Samuel Beckett (via oisinbyrne)

stokes: Pixar nearly lost Toy Story 2 to a bad backup

Fri, 11 May 2012 11:03:59 +0100

stokes:

Pixar nearly lost Toy Story 2 to a bad backup

A Web Developer link for a change, funny out

Thu, 10 May 2012 17:07:01 +0100

A Web Developer link for a change, funny out

Nice work from cousin.. Set to Rise : Brid Og Norrby

Thu, 03 May 2012 16:14:03 +0100

Nice work from cousin.. Set to Rise : Brid Og Norrby

Nice, Repeat Repeat Repeat, Patterns Patterns Patterns

Thu, 03 May 2012 10:00:14 +0100

Nice, Repeat Repeat Repeat, Patterns Patterns Patterns

Turner prize shortlist 2012 - in pictures

Tue, 01 May 2012 17:09:44 +0100

Turner prize shortlist 2012 - in pictures

Visions of Cities without people

Tue, 01 May 2012 15:01:49 +0100

Visions of Cities without people

lifeisjustatheory: fuckyeahmolecularbiology: So What Is a...

Wed, 25 Apr 2012 13:52:30 +0100

lifeisjustatheory:

fuckyeahmolecularbiology:

So What Is a Fractal, Anyway?

It is my firm conviction that mathematics underpins everything in the universe. Mathematics was intrinsically designed to explain the world; Newton invented differential and integral calculus, for example, to explain why the orbits of the planets were in the shape of an ellipse. Understanding the mathematics behind phenomena will not make them any less beautiful; it will make them more beautiful in that the complexity of our world is better understood and appreciated.

To put it simply, fractals are self-similar and have an unusual relationship with space - kind of like the ‘It’s Complicated’ relationship status on Facebook. Self-similar, in this case, means that fractals have something called irreducible complexity: No matter how far you “zoom in” to a fractal pattern, the structure will be exactly or approximately similar to the fractal itself. In order to understand a fractal’s unusual relationship with space, however, we’re going to need to consider the concept of dimensions.

Dimensions, in their simplicity, are a very interesting mathematical concept. What, for example, makes a line one-dimensional, and a plane two-dimensional? Note that lines and planes are both self-similar, as outlined by the definition above. The differences actually lie in their self-similarity; a line can be broken down into N self-similar pieces, each with a magnification factor of N; a plane can be broken down into N^2 similar pieces, each with a magnification factor N; and a cube into N^3 pieces, with the same magnification factor N. A magnification factor will be defined here as the amount you have to “zoom in” to regain the original structure.

Therefore, dimensions of self-similar objects are simply the exponent of the number of self-similar pieces with magnification factor N into which the figure may be broken. So the line segment mentioned before exists in one dimension; the plane in two dimensions; and the cube in three dimensions. Not too bad, right?

Well, here’s the complicated part. Fractals can exist in non-integer dimensions.

For example, we can consider the Sierpinski Triangle, which looks like this:

If we accept our original ideas about dimensions to be valid, then the dimension of the Sierpinski Triangle - which, by our definition, exhibits a fractal pattern - would be governed by:

Fractals have an “unusual relationship with space” because they - as shown by the Sierpinski Triangle - can exist in non-integer dimensions. Amazing, right?

The three bottom images above are taken from the Mandelbrot Set - which has a topological dimension of 2 (meaning that it’s visualised, and pictured, in two dimensions) but has a fractal dimension that’s much more complex. Fractals from the Mandelbrot set - and other fractal patterns - are found throughout nature, including in the growth patterns of bacteria at the top of this post! Other examples include unfurling ferns, and the inside of certain types of seashells. It’s even been shown that the small motions of our eyes follow a fractal pattern - which is why we find things that exist in a fractal pattern aesthetically pleasing.

Next time you see a fractal pattern, remember that it doesn’t just exist topologically as you see it - it’s fractal dimension could be 1.58, or 1.7! The maths behind fractal images are just as beautiful as the images themselves. In fact, in my opinion they enhance the beauty of the images my eye naturally finds aesthetically pleasing.

Images: The top two images shown are of bacteria cultures exhibiting fractal growth due to environmental stress. The bottom three images are from the Mandelbrot Set.

Great explanation!

Photo

Tue, 20 Mar 2012 10:11:19 +0000

C215 hits the streets of Dublin

Wed, 14 Mar 2012 09:41:41 +0000

C215 hits the streets of Dublin

zanthi: Stencils by French street artist Christian Guémy aka...

Wed, 07 Mar 2012 17:00:35 +0000

zanthi:

Stencils by French street artist Christian Guémy aka C215 as seen on the streets of Berlin and Barcelona.

Circle X

Sat, 03 Mar 2012 16:36:06 +0000

Circle X

Spirals at Newgrange

Sat, 03 Mar 2012 14:24:06 +0000

Spirals at Newgrange

Circle IX

Sat, 03 Mar 2012 12:12:06 +0000

Circle IX

Circle VIII

Fri, 02 Mar 2012 18:48:05 +0000

Circle VIII

wrk-kevintownsend: while I was away, sketchbook pages: set...

Fri, 02 Mar 2012 16:36:09 +0000

wrk-kevintownsend:

while I was away, sketchbook pages: set 4
KEVIN TOWNSEND