payload

The original snake game is one of the simplest and best-known video games of all time. It was one of the first games available on personal computers and it came pre-installed on early Nokia phones. The idea is to guide a snake on a 2D grid so that it doesn’t crash into itself. At the same time, points are earned by running into items and eating them – but doing so makes the snake longer and harder to navigate. Deceptively simple, snake requires strategic forethought and super-quick reflexes.
For snake game lovers – and those who missed out – software engineer Andrey Fedoseev at the London Institute has developed a 3D version of snake. It’s free and can be played on phones and laptops. Snake 3D is a lot more challenging than the original 2D version because it tests your spatial visualization. It can be played with or without perspective, and the point of view can be rotated in real-time. Instead of crashing into walls, in Snake 3D the snake passes on through them to the other side. With multiple levels that become increasingly tough, 3D Snake brings an extra dimension to the original cult classic.
<a href="https://snake3d.netlify.app">Try it now</a>!

Snake 3D is a free multi-level video game that brings an extra dimension and a lot more challenge to the cult-classic game of snake.

Snake 3D

Highly divisible numbers are useful whenever a whole needs to be divided into equal parts in different ways. For example, 60 can be divided in 12 different ways. But often it is necessary to divide the parts into subparts, and subparts into sub-subparts, and so on, in a recursive way. For example, 72 can also be divided in 12 different ways but, unlike 60, the resultant subparts tend to be themselves highly divisible, as do the resultant sub-subparts, and so on. Researchers at the London Institute have discovered numbers which are divisible in this recursive way and call them recursively divisible numbers.
The extent to which a number is recursively divisible can be visualized by drawing its divisor tree. 
The more squares there are in the divisor tree, the more recursively divisible the number is. 
We made a web application that draws divisor trees for any given number. Divisor trees that have more squares than any of their predecessors, such as 72, 96, 120, 144 and 192, are called highly recursively composite. These numbers are especially useful for modular grid systems in graphic and digital design.
<a href="https://lims.ac.uk/recursively-divisible-numbers/">Try it now</a>

A way to visualize recursively divisible numbers, a new kind of number for modular design that can be broken into parts hierarchically.

Divisor trees

Some numbers are more interesting than others. For instance, 6 is the first perfect number, meaning that it is the first number equal to the sum of its proper divisors. When G. H. Hardy suggested the number 1729 of the taxi he had ridden was dull, Ramanujan set him straight, noting it is the smallest number that is the sum of two cubes in two ways. The Penguin Dictionary of Curious and Interesting Numbers lists 51 as the “first uninteresting number”—paradoxically making it notable. A more concrete definition of uninterestingness is the smallest integer not to appear in any entry of the On-Line Encyclopedia of Integer Sequences: 17,843 at the time of writing.
The London Institute’s Christmas card gives a mathematical interpretation of “The Twelve Days of Christmas”. Remarkable properties of the numbers 1 to 12 are described and illustrated, from 1 side to the Möbius strip to 5 exceptional Lie groups and beyond. The card was parametrically drawn by Robert Farr and written by Thomas Fink. It was sent to everyone who has supported us over the past year. We’re grateful for all your help and encouragement.

The Institute’s Christmas card includes one side to the Möbius strip, five exceptional Lie groups and eight basis vectors of the octonians.

Twelve Days of Christmas

When tiles can be arranged to cover the plane without gaps or overlaps, they are said to tile the plane. It was thought that all tiles which can tile the plane can do so periodically, meaning that the tiling could be rebuilt by translating a finite region of it. However, in the 1960s it was discovered that certain sets of tiles must tile the plane in an aperiodic way: the pattern never repeats, even out to infinity. The original such set comprised 20,426 different types of tile, but this number was whittled down until mathematician Roger Penrose discovered his two-tile set.
The London Institute entrance hall is tiled with white Carrara marble and black obsidian in the shape of Penrose tiles. Not shown is a set of edge-matching rules in the form of two positive and negative notches per tile. The Penrose tiling has approximate five-fold rotational symmetry, like a pentagon; and although it never repeats when translated, similar patterns occur at larger and larger scales as the tiling is built out. This symmetry-on-magnification is a theme in several research projects at the Institute, and leads to the concept of fractal dimension.

Our entrance hall floor is a Penrose tiling, an aperiodic crystal that never repeats, made from white Carrara marble and black obsidian.

Never-repeating crystal

The London Institute’s logo is based on a carving from the Institute’s 18th-century fireplace in its seminar room: a classical lamp with snakes either side. The lamp is in the manner of Robert Adam and resembles a classical urn. Carried by Diogenes during the day in search of an honest man, the lamp has come to symbolize knowledge and learning. Surrounding the lamp is a dark blue annulus which bears the Institute's name in white Palatino: London Institute for Mathematical Sciences.
Inside the annulus is the Institute’s motto, “Truth, Beauty,” in gold ITC Blair. In the penultimate line of his poem "Ode on a Grecian Urn," John Keats writes that "Beauty is truth, truth beauty". These words are a reference to the observation that the universe is described by surprisingly elegant mathematics. One of the mysteries of physics is that mathematical beauty is a curiously effective indicator of physical truth. Researchers at the London Institute seek new insights not just for their utility, but also to enrich the world of ideas, which contains its own internal beauty.

The logo of the London Institute is based on a classical lamp with snakes either side and shows the Institute’s motto, “Truth, Beauty”.