Pictures of Math

[itscolossal]

WATCH: A Kinetic Sculpture of 15 Moving LEDs Mimics a Walking Person [video]

[isomorphismes]

Drawings of random geometry by Boris Hanin

[matthen]

a visual proof that ¼ + 1/16 + 1/64 + … = 1/3 [code] 

[matthen]

A dodecahedron tumbling inside a circumscribing circle. [code]

[matthen]

The primes are often thought of as behaving like a random sequence, but there are patterns in their digits. The first frame shows how many of the first 100 primes end in 1, 3, 7 and 9. They all occur roughly the same number of times, so the four squares are almost exactly the same shade of red. The next frame shows how frequently a prime ending in 1 is followed by a prime ending in 3 - and so on. A structured pattern emerges, with the final frame showing the distribution of final digits in strings of 8 consecutive primes (for the first 2 million primes).  [recent news] [visualization from] [code]

[itscolossal]

WATCH: Crank Out Infinite Geometric Designs With The Wooden Cycloid Drawing Machine (video)

[picturesofmath]

mmmm

[fuckyeahfluiddynamics]

These golden lines reveal the complexity of turbulent convective flow. They come from a numerical simulation of turbulent Rayleigh-Benard convection, a situation in which fluid trapped between two plates is heated from below and cooled from above. This situation would typically create convection cells similar to those seen in clouds or when cooking. Inside these cells, warm fluid rises to the top, cools, and sinks down along the sides. With large enough temperature differences, instabilities will occur and cause the flow to become turbulent so that the clear structure of convection cells breaks down into something more chaotic. Such is the case in this simulation. This visualization shows skin friction on the bottom (heated) plate in a flow of turbulently convecting liquid mercury. The bright lines are areas with large velocity changes at the wall, an indication of high shear stress and vigorous convective flow. (Image credit: J. Scheel et al.; via Gizmodo)

[itscolossal]

A 3D Printed Sundial Displays Time Like a Digital Clock

[fuckyeahfluiddynamics]

Cymatics are the visualization of vibration and sound. Here photographer Linden Gledhill has taken a simple speaker vibrating a dish of water and turned it into some incredible art. When you vibrate liquids like water up and down, it disturbs the usually flat air-water interface and creates waves on the surface. These Faraday waves are a standing wave pattern that differs depending on which sound is being played. By combining the wave patterns with LED lighting and strobe effects, Gledhill creates some remarkable images that combine sound, light, and fluid dynamics all in one. If you watch the video (make sure to hit the HD button!), you’ll see the patterns in motion and hear the sounds used to generate them. In the last clip (around 0:19), he’s added glitter to the set-up, which highlights the circulation within the vibrating fluid. As you can see, there are strong recirculating regions in each lobe of the pattern, but other areas, like the center region are almost entirely stationary. You can see more photos from the project in his Flickr feed. Special thanks to Linden for letting me post the video of his work, too! (Video and image credits and submission: L. Gledhill)

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[laughingsquid]

A Chameleon Robot That Can Quickly Change Color to Blend In With Different Backgrounds

[laughingsquid]

10,000 Dominoes Arranged as a Working Computer Circuit Capable of Performing Basic Addition

[picturesofmath]

Long video but so cool 😍🤓

[a-na5]

[isomorphismes]

Limit set of Maskit’s version of the 11/120 double cusp group. (The colored circle chain reveals the fraction 11/120.)

by David J. Wright

[malinchristersson]

An epicycloid with one cusp rolling inside an epicycloid with two cusps rolling inside an epicycloid with three cusps rolling inside…

Interactive versions

[vimeo-deactivated20240328]

What’s happeninggggg?? 

[bigblueboo]

snappers

[itscolossal]

Pluto Through the Years: A GIF Showing Gradually Improved Views of Pluto from 1930-2015