sciencesourceimages:

How Mandelbrot’s Fractals Changed The World

by Jack Challoner/BBC News

During the 1980s, people became familiar with fractals through those weird, colorful patterns made by computers. But few realize how the idea of fractals has revolutionized our understanding of the world, and how many fractal-based systems we depend upon.

Unfortunately, there is no definition of fractals that is both simple and accurate. Like so many things in modern science and mathematics, discussions of “fractal geometry” can quickly go over the heads of the non-mathematically-minded. This is a real shame, because there is profound beauty and power in the idea of fractals.

The best way to get a feeling for what fractals are is to consider some examples. Clouds, mountains, coastlines, cauliflowers and ferns are all natural fractals. These shapes have something in common - something intuitive, accessible and aesthetic.

They are all complicated and irregular: the sort of shape that mathematicians used to shy away from in favor of regular ones, like spheres, which they could tame with equations.

Mandelbrot famously wrote: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

The chaos and irregularity of the world - Mandelbrot referred to it as “roughness” - is something to be celebrated. It would be a shame if clouds really were spheres, and mountains cones.

Look closely at a fractal, and you will find that the complexity is still present at a smaller scale. A small cloud is strikingly similar to the whole thing. A pine tree is composed of branches that are composed of branches - which in turn are composed of branches.

Read the entire article

Fractal images © Laguna Design / Science Source

Mandelbrodt photo © Emilio Segrè / Science Source

Sit, be still, and listen, because you’re drunk and we’re at the edge of the roof.
Rumi (via thecalminside)
We’re all kids in grown-up bodies. #dontforgettoplay

We’re all kids in grown-up bodies. #dontforgettoplay

When I’m 80… #california #foreveryoung

When I’m 80… #california #foreveryoung

Be a part of the great Internet Slowdown

fight4future:

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On September 10th, just a few days before the FCC’s net neutrality comment deadline, internet users and tech companies will unite for the “Internet Slowdown” to show the world what’s at stake if we lose net neutrality, the “First Amendment of the Internet.”

staff:

Today’s the day. The day you help save the internet from being ruined.

Ready? 

Yes, you are, and we’re ready to help you.

(Long story short: The FCC is about to make a critical decision as to whether or not internet service providers have to treat all traffic equally. If they choose wrong, then the internet where anyone can start a website for any reason at all, the internet that’s been so momentous, funny, weird, and surprising—that internet could cease to exist. Here’s your chance to preserve a beautiful thing.)

May the universe in some strange sense be “brought into being” by the participation of those who participate? The vital act is the act of participation. “Participator” is the incontrovertible new concept given by quantum mechanics. It strikes down the term “observer” of classical theory, the man who stands safely behind the thick glass wall and watches what goes on without taking part. It can’t be done, quantum mechanics says. — John Wheeler

May the universe in some strange sense be “brought into being” by the participation of those who participate? The vital act is the act of participation. “Participator” is the incontrovertible new concept given by quantum mechanics. It strikes down the term “observer” of classical theory, the man who stands safely behind the thick glass wall and watches what goes on without taking part. It can’t be done, quantum mechanics says. — John Wheeler

01001100 01101001 01100110 01100101 #California

01001100 01101001 01100110 01100101 #California

whisperingwordsofwisdom:


“She was always a little bit surprised by the efforts women made to look young. She was actually very happy about growing older because it meant more time for herself, more time for her family, and separation from the frenzy of youth and beauty that is Hollywood. She was very strict about everybody’s time in life.” -Luca Dotti remembers his mother Audrey Hepburn. (Left: Audrey Hepburn circa 1957. Right: Audrey Hepburn in 1990)


No Botox, no surgery, just grace.

whisperingwordsofwisdom:

She was always a little bit surprised by the efforts women made to look young. She was actually very happy about growing older because it meant more time for herself, more time for her family, and separation from the frenzy of youth and beauty that is Hollywood. She was very strict about everybody’s time in life.” -Luca Dotti remembers his mother Audrey Hepburn. (Left: Audrey Hepburn circa 1957. Right: Audrey Hepburn in 1990)

No Botox, no surgery, just grace.

…and I want to beg you, as much as I can, to be patient toward all that is unsolved in your heart and to try to love the questions themselves like locked rooms and like books that are written in a very foreign tongue…Live the questions now. Perhaps you will then gradually, without noticing it, live along some distant day into the answer.
—Rainer Maria Rilke, "Letters on Love" (via wreckandsalvage)
The imagination is not a state,
it is the human existence itself.
William Blake (English, 1757-1827)
"…they paved paradise and put up a parking lot…🎶"

"…they paved paradise and put up a parking lot…🎶"

The antagonist always believes they are the protagonist.
Thoughts on dualism at 3am