After a nearly 40-year chase, physicists have found experimental proof for one of the first fractal patterns known to quantum physics: the Hofstadter butterfly. Named after Douglas Hofstadter, the Pulitzer prizewinning author of the 1979 book Gödel, Escher, Bach, the pattern describes the behaviour of electrons in extreme magnetic fields.
“As a huge fan of photography and admiring Benoit Mandelbrot’s genius since college, I believe fractals are one of the most brilliant depiction of intelligence. Sadly we lost him last year, but we will never lose his work!”
(Cool screensaver. Thanks for the photo, Silvia!)
In a 1996 interview, David Foster Wallace (a student of advanced mathematics in college in addition to being, you know, a writer) revealed that the structure of his career-defining work Infinite Jest was devised as a literary fractal.
It’s actually structured like something called a Sierpinski Gasket, which is a very primitive kind of pyramidical fractal, although what was structured as a Sierpinski Gasket was the first- was the draft that I delivered to [my editor] Michael in ‘94, and it went through some I think ‘mercy cuts’, so it’s probably kind of a lopsided Sierpinski Gasket now.
This Serpinski Gasket that he speaks of? The ordered wormhole of symmetrical layers? It’s a famous construction of stacked triangles that you’ve probably seen before.
Want to dig really deep into the literary mathemagic behind Wallace’s work? Here’s a fantastic essay in the Los Angeles Review of Books (warning: pretty cerebral). DFW reminds us:
“God has particular languages, and one of them is music and one of them is mathematics.”
(Tip of the triangle to Maria Popova)
The Mandelbrot set Paradox.
Published on Sep 15, 2012 by nickharvey7
We have this paradox because the Mandelbrot Set is covered by a finite area, but has an infinite outer boundary. In fact, there are no two distinct points on the boundary of the Mandelbrot Set that can be reached from one another by moving a finite distance along that boundary. This paradox can be explained by explaining a potential infinity of possibilities formed from a dynamic universal geometry that human mathematics itself is based upon. In this theory fractals are formed by the repetition of the quantum wave particle function or probability function of quantum mechanics continuously collapsing and reforming. A kind of geometrical and therefore mathematical repetition!
We have infinite complexity upon the boundary of a fractal like the Julia Sets.
No matter how much we magnify a fractal we will still see new patterns new images immerging. In this theory this is because we have an interactive process the fractals are only relative to actions of the mathematician. We have a process of continuous creation or change creating an infinity of possibilities at every degree and angle of creation that we can interact with turning the possible into the actual!
Work by Jason Padgett, a man with Acquired Savant Syndrome who now sees all of reality as mathematical fractals describable by equations.
The beauty of numbers and their connection to the pure geometry of space time and the universe is shown in his fractal diagrams…He is currently studying how all fractals arise from limits and how E=MC2 is itself a fractal. When he first started drawing he had no traditional math training and could only draw what he saw as math. Eventually a physicist saw his drawings and helped him get traditional mathematics training to be able to describe in equations the complex geometry of his drawings. He is currently a student studying mathematics in Washington state where he is learning traditional mathematics so he can better describe what he sees in a more traditional form. Many of the captions were written before he had any traditional math training. His drawing of E=MC^2 is based on the structure of space time at the quantum level and is based on the concept that there is a physical limit to observation which is the Planck length. It shows how at the smallest level, the structure of space time is a fractal…So sit back and enjoy the beauty of naturally occuring mathematics in pure geometric form connecting E=MC2 (energy) to art. All are HAND DRAWN using only a pencil, ruler and compass.
These are amazing!
if you want to get fractals read Dr. Seuss
Google Earth: source of information, source of wonder, source of art. In 2010, Paul Bourke, a research associate professor at the University of Western Australia, began using the service to capture images for his ongoing Google Earth Fractals series. Since then, he’s amassed an amazing collection of space-based photographs that are equal parts science and beauty: Each intoxicating image on the project’s website is accompanied by a KMZ file that lets users pinpoint the photos’ locations on their own Google Earth viewers, putting them in geographic as well as aesthetic context.
See more. [Images: Google Earth]
Fractal pancakes and organ pancakes! Now I know what’s been missing from my morning routine all these years. These are from Saipancakes and if you’re not satisfied with what you see here, don’t worry, they have lots more.
…those lungs look extra tasty, don’t they?
This article was published by Wired on December 9, 2009. This is not a new news but I still find it amazing. The first time I saw this, I was like, “WHOOAAH! These are beautiful!”
This article was about the Mandelbulb. A group of math geeks created a three-dimensional analogue for the mesmerizing Mandelbrot fractal. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.
|—||Benoit Mandelbrot (via laisidhiel)|