La manzana Cuántica de Einstein @rivarius - Tumblr Blog

A few plots of sandpile toppling. The typical rule is any cell with 4 or more grains topples by sending one to each neighbor. In general this kind of cellular automata is known as “chip firing” and is Abelian meaning unstable cells can be toppled in any order or even in parallel and still reach the same final state.

These plots are produced by dropping a million grains on the very center cell and having it all topple until stability. The cells are colored by how many grains of sand are on it. The different results come from changing the toppling rules; how many a cell can hold and how many go to each neighbor. Absolutely fascinating structure!

vedalkensamurai

Chapter V

z_(n+1) = z_n² * e^z_n^t + z_n^-2 * e^-z_n^t + c

t grows from 5 to 6. Rotated 90° clockwise.

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nasa

Mathematician. Leader. Heroine. Remembering Hidden Figure Katherine Johnson

Tonight, count the stars and remember a trailblazer.

We’re saddened by the passing of celebrated #HiddenFigures mathematician Katherine Johnson. She passed away at 101 years old.

An America hero, Johnson’s legacy of excellence broke down racial and social barriers while helping get our space agency off the ground.

Once a “human computer”, she famously calculated the flight trajectory for Alan Shepard, the first American in space.

And when we began to use electronic computers for calculations, astronaut John Glenn said that he’d trust the computers only after Johnson personally checked the math.

As a girl, Katherine Johnson counted everything. As a mathematician, her calculations proved critical to our early successes in space travel.

With slide rules and pencils, Katherine Johnson’s brilliant mind helped launch our nation into space. No longer a Hidden Figure, her bravery and commitment to excellence leaves an eternal legacy for us all.

“We will always have STEM with us. Some things will drop out of the public eye and will go away, but there will always be science, engineering and technology. And there will always, always be mathematics.” - Katherine Johnson 1918 -2020

May she rest in peace, and may her powerful legacy inspire generations to come! What does Katherine Johnson’s legacy mean to you? Share in the comments.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

curiosamathematica

Frieze groups

The frieze groups are used to classify patterns which are repetitive in one direction, according to their symmetries. Of course, such designs occur frequently in architecture and decorative art. Mathematical study of such patterns reveals that essentially, only seven types of symmetry can occur.

The first frieze group, coined HOP by John Conway, is generated by a single translation and therefore contains only translational symmetries:

The second group, STEP, contains translation and glide reflection symmetries. This group is singly generated as well, by a glide reflection (as a translation can be simulated by two glide reflections).

SIDLE contains translation and vertical reflection symmetries.

Next, a SPINNING HOP is generated by a translation and a 180° rotation.

SPINNING SIDLE contains translation, glide reflection and rotation (by a half-turn) symmetries.

JUMP contains translation and horizontal reflection symmetries.

Finally, SPINNING JUMP contains all symmetries (translation, horizontal & vertical reflection, and rotation). This group requires three generators, for instance a translation, the reflection in the horizontal axis and a reflection across a vertical axis.

spring-of-mathematics

Happy International Women in Math Day ! 12/05

Today, we remember Maryam Mirzakhani and the impact she had (and continues to have) on women in math.

SEE MORE at: 11 Famous Women Mathematicians and Their Incredible Contributions! by Anthony Persico

mathani

A square grid in polar (r, φ) coordinates stretches into a curved grid in the xy-plane. Patches farther from the r = 0 line stretch more, while those close to the line can contract. This is exactly what is captured by the Jacobian, and why it appears when one changes variables in a double integral.

materialsscienceandengineering

3D 'polar chiral bobbers' identified in ferroelectric thin films

A novel type of three-dimensional (3D) polar topological structure, termed the "polar chiral bobber," has been discovered in ferroelectric oxide thin films, demonstrating promising potential for high-density multistate non-volatile memory and logic devices. The result was achieved by a collaborative research team from the Institute of Metal Research (IMR) of the Chinese Academy of Sciences, the Songshan Lake Materials Laboratory, and other institutions. The findings were published in Advanced Materials on January 30. Topological polar textures in ferroelectrics, such as flux-closures, vortices, skyrmions, merons, Bloch points, and high-order radial vortices discovered in recent years, have attracted wide interest for future electronic applications. However, most known polar states possess limited configurational degrees of freedom, constraining their potential for multilevel data storage.

vedalkensamurai

Dense Foliage

z_(n+1) = z_n ^ (i * z_n) + c

z₀ = c

100,000,000 random complex values of c; 32 iterations for red, 256 for green, 64 for blue.

Welcome to the jungle

vedalkensamurai

z_(n+1) = i^(4t) * sin(z_n) + c if n is even

z_(n+1) = i^(-4t) * sinh(z_n) + c if n is odd

t grows from 0 to 1.

evil-jennifer-hamilton-wb

Reblogging this from the r/mathmemes subreddit because it's fun

A square:

more-mathematics-mor-lam

New special interest unlocked: diagrams of prerequisites

functor-reality

I have another one for you

sevenfactorial

I have a story before getting to a prereq diagram.

One of my friends in undergrad had the smart idea of making a diagram for the math class prereqs. Then one of our professors (one who tended to mentor undergrads) made some improvements and also made it in tikz because... that really is just who she is. It becomes an unofficial but useful resource math club passed out at informal advising night.

Later, when me and a different friend were on the math club leadership board, we decided to update the diagram (after recreating it not in tikz), plus we made diagrams customized for all three versions of the math degree. Because there were three different bachelor's of science in mathematics you could get? Idk. We also made one for the grad level classes.

Unfortunately, posting these (absolutely fantastic and meticulous) flowcharts is a little bit too close to doxxing myself.

BUT there is still a prereq diagram left which I can share far and wide under my pseudonym!

At some point, I decided to make a diagram for the computer science classes and got this bemusing mess:

learning-is-underrated

physicallyimprobable

I would like to humbly submit the chapter diagram for my own WIP (early-planning stages) popmath book about infinities. Not intended to be shown to readers, but useful for me to like, think about the structure of things.