Q:Question: As an artist I am fascinated by a pattern I see repeated throughout nature. Surely there must be a physic's law that is causing it? Tree branching/root systems, circulatory systems, nervous system, river branching, lightening patterns. The "branching" pattern is everywhere. What is that called and why does it show up everywhere? I am an artist obsessed with trees at the moment and if I can understand this concept my artwork will improve! Thanks Destin!
I want a word for this as well!
This NASA Earth Oservatory shot of Canyon de Chelly in Arizona illustrates this tree-like branching pattern quite well.
While fractals are certainly at play in these sort of natural patterns, mathematicians have a more specific term for this specific branching/sub-branching behavior: “ramification”.
Here’s a scientific study on the ramification of river networks, so you can see how they’re made. The magic number is 72˚.
To celebrate the puzzle’s 40th anniversary, today’s Google Doodle is a fully-functional Rubik’s Cube! If you had a cube for every possible arrangement of the 54 colored squares, and you laid them end-to-end, those 43,252,003,274,489,856,000 cubes would extend 261 light years.
But no single Rubik’s cube can be configured to all of those Rubik’s universes.
If the traditional cube isn’t challenging enough for you, you can head over to the Chrome Cube Lab and try your digital hand at some other cubic puzzles.
The folks at Numberphile took an in-depth look at the math behind a Rubik’s Cube in a series of videos on YouTube. Here’s one of them:
Putting the “pi” in “piano”
Check out this awesome piano melody created from the digits of pi! By transposing the numbers 0-9 onto an A minor scale, the irrational melody is played with the right hand and notes are added with the left. It’s pretty mathemagical.
Also, try singing this along with the melody, either out loud or in your head (it totally works):
"I am listening to a sonnnnng about piiiiiii, maaaaking a melody as the numbers fly byyyyy"
Bonus: Check out Daniel Starr-Tambor’s “Mandala”, a melody created from the orbits of the planets placed onto a musical scale. At 62 viginitillion notes (I didn’t even know that was a number), it’s the longest palindrome ever created.
Helen Friel - “Here’s Looking at Euclid” (paper sculptures of mathematician Oliver Byrne’s illustrations of Euclid’s Elements, 2012)
Byrne’s illustrated Euclid is one of my favorite vintage science reads (you can leaf through it online for free!) and the fact that the Mondrain-esque artwork has been made into paper sculptures makes me happier than I can verbalize.
Welcome to Infinity
Can you imagine a more perfect thing than Arthur C. Clarke narrating a film about fractals and the Mandelbrot Set, with a soundtrack created by Pink Floyd’s David Gilmour?
Featuring interviews with Benoit Mandelbrot and Stephen Hawking?
Because that is a thing that exists. It’s right up there, just press play. Thanks to Open Culture for posting this. Enjoy!
To celebrate, here’s a Mandelbrot Set GIF:
Oh, did you guys hear the joke about Benoit B. Mandelbrot’s middle name?
The Genius of J.S. Bach’s “Crab Canon” Visualized on a Möbius Strip
We know J.S. Bach was a genius composer. Certainly among the top two or three that have ever lived by most measures. Even knowing that, I was not prepared for the awesomeness you are about to see.
This is the first canon from Bach’s Musical Offering, known as the “crab canon”. The first level of awesome is when you find out that it was designed to be played backwards and forwards. But lots of people have done that … big deal, right?
Then you find out that it was written to be played backwards and forwards at the same time. That’s pretty amazing, but again, since it’s not that long I wouldn’t classify it as an Earth-shattering epiphany.
BUT THEN … graphic artist Jos Leys (who made the video), show how this Bach piece is basically the musical version of a Möbius strip.
(Read more at Open Culture)
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.
Holy cow, is this what Neo saw in The Matrix?