The beauty of mathematics – in pictures

The book 50 Visions of Mathematics is a collection of 50 short essays by 50 maths writers and a foreword by Dara O Briain. Launched on Wednesday to celebrate the 50th anniversary of the Institute of Mathematics and its Applications, it also contains 50 images supplied in response to an open call from the worldwide maths community. Here are my favourites

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• Alex Bellos
• theguardian.com, Wednesday 14 May 2014 07.00 BST

The Brillouin zones of a square crystal lattice in two dimensions, which underlie the analysis of waves propagating through the crystal. Image: R R Hogan, University of Cambridge

A trefoil knot combining four parallel Möbius strips and a spiral tube running continuously round. Drawn freehand by Tom Holliday, inspired by M C Escher

A 3D print of the tesseract, which is the four dimensional analogue of the cube. Sculpture by Saul Schleimer and Henry Segerman. Photograph: Henry Segerman

The Mandelbox is a 3D fractal object that represents the points in space that do not move to infinity under the action of a set of geometric transformations. Image: Jos Leys

A much-magnified detail of the Mandelbrot set, revealing what appears to be a procession of elephants. Image by Philip Dawd, using the program winCIG Chaos Image Generator developed by Thomas Hvel. Copyright: Darwin College, University of Cambridge

Bat country, a 22ft tall Sierpinski tetrahedron composed of 384 softball bats, 130 balls, and a couple of thousand pounds of steel. Designed by Gwen Fisher, engineered by Paul Brown. Photograph: Gwen Fisher

A representation of 3,000 seeds on a sunflower with spirals occuring a Fibonacci number of times: 1, 1, 2,3, 5, 8, ... Image: Ron Knott

A crocheted model of the hyperbolic plane. Photograph: Daina Taimina

Map showing areas around Cambridge accessible via public transport, visualised in time bands of ten minutes, with a departure time of 9am. Image: Mapumental

A quaternion Julia set fractal. With the advent of 3-D printing, mathematical constructs like this can now be printed as physical objects, like the one below. Image: Rob Hocking

A model of the Julia set in gold-plated brass. Photograph: Rob Hocking

A hybrid 3-D fractal object, obtained using a combination of two sets of geometric transformations. Image: Jos Leys

The complex folding patterns that arise when a layered material (paper) is put into a test machine and squashed. Created by Timothy Dodwell and Andrew Rhead, University of Bath

A demonstration of the mathematical principles of the original Forth Bridge in Scotland performed at Imperial College in 1887. The central 'weight' is Kaichi Watanabe, one of the first Japanese engineers to study in the UK, while Sir John Fowler and Benjamin Baker provide the supports. Photograph: Imperial College

Long-exposure photograph of a double pendulum exhibiting chaotic motion. Photograph: Michael G Devereux

The proof is in the pudding: cake illustration of Pythagoras's theorem, baked by Emiko Dupont. Photograph: University of Bath