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3D printing used as a tool to explain theoretical physics

Students may soon be able to reach out and touch some of the theoretical concepts they are taught in their physics classes thanks to a novel idea devised by a group of researchers from Imperial College London.

In new study published today, 9 December, in the journal EPL, the researchers have successfully demonstrated how complex theoretical physics can be transformed into a physical object using a 3D printer.

Researchers have successfully demonstrated how complex theoretical physics can be transformed into a physical object using a 3D printer.

Credit: Imperial College London/EPL

In just eight hours and at the cost of around 15 euros, they were able to use a commercially available 3D printer to create their own 8 cm3 object based on a mathematical model that described how forest fires can be started and how they eventually spread over time.

The researchers have labelled the approach "Sculplexity"—standing for sculptures of complexity—and believe it could also be used to produce works of art based on science, or transform the way that ideas and concepts are presented and discussed within the scientific community.

Co-author of the study Dr Tim Evans, a theoretical physicist at Imperial, said: "The work was inspired by a visit to the Victoria and Albert Museum in London where I came across the first ever 3D printed object the museum had acquired.

"The object was a table inspired by the tree-like structures found in nature, which is an example of a branching process that is commonly encountered in complex systems in theoretical physics. This led me to think, what other processes familiar to physics could be turned into a 3D printed object?"

Complex systems are made up of many parts that interact on many time and length scales and which show coherent behaviour and certain patterns on a large scale. A living organism is the best example of a complex system, whereby the individual parts—in this case the molecular processes in the cell — interact with each other and contribute to much larger processes on a macroscopic scale.

The interactions at play in many complex systems can be mapped out onto a two-dimensional grid which is divided into identical squares, or "cells". Each of the cells can exist in a certain state and evolve over time, which is governed by a certain set of rules.

In their study, the researchers used a forest fire as an example, in which each cell represented a tree which could either be alive, dead or burning. The exact state that each cell occupied over time depended on a set of rules, which took into account the cell's proximity to other cells that may be burning or if it was struck by lightning.

"The basic idea is simple," continued Dr Evans. "A 3D printer builds up its object in layers. So the height of the object can be thought of as time. Suppose you have a mathematical model which defines a flat, two-dimensional picture that evolves in time — typically this will be a grid with some squares full and some empty.

"The mathematical model will define at each point in time what the printer should print at one height. The next step in the model will then define what to print on top of the first layer, and so forth. The result is a 3D object which shows how the mathematical model has evolved over time."

The resulting model the researchers created was not without glitches; however, Dr Evans believes the experience has allowed them to identify the obstacles, formulate solutions and inspire the physics community to "get creative".

"In our own group at Imperial we are trying to explain heartbeat anomalies by looking at simple models for the behaviour of individual cells in heart muscle — it's possible that this could be visualised using 3D printing. Most models that represent the spread of disease could also be visualised.

"There may be many other examples and we just hope our rather literal translation from theoretical model to 3D printer output stimulates others to get creative," Dr Evans concluded.

From Monday 9 December the paper can be downloaded from

Notes to Editors


1. For further information, a full draft of the journal paper or contact with one of the researchers, contact IOP Press Officer, Michael Bishop:
Tel: 0117 930 1032
For more information on how to use the embargoed material above, please refer to our embargo policy.

IOP Publishing Journalist Area

2. The IOP Publishing Journalist Area gives journalists access to embargoed press releases, advance copies of papers, supplementary images and videos. In addition to this, a weekly news digest is uploaded into the Journalist Area every Friday, highlighting a selection of newsworthy papers set to be published in the following week.

Login details also give free access to IOPscience, IOP Publishing's journal platform.

To apply for a free subscription to this service, please email Michael Bishop, IOP Press Officer,, with your name, organisation, address and a preferred username.

Sculplexity: Sculptures of complexity using 3D printing

3. The published version of the paper "Sculplexity: Sculptures of complexity using 3D printing" will be freely available online from Monday 9 December. It will be available at


4. EPL is published under the scientific policy and control of the European Physical Society by the Société Française de Physique (SFP) and its subsidiary EDP Sciences, the UK Institute of Physics (through IOP Publishing) and the Società Italiana di Fisica (SIF), for a partnership of 17 European physical societies (the EPL Association).

It publishes original, high-quality Letters in all areas of physics, ranging from condensed matter topics and interdisciplinary research to astrophysics, geophysics, plasma and fusion sciences, including those with application potential. Articles must contain sufficient argument and supporting information to satisfy workers in the field, and must also be of interest and relevance to wider sections of the physics community.

IOP Publishing

5. IOP Publishing provides a range of journals, magazines, websites and services that enable researchers and research organisations to reach the widest possible audience for their research.

We combine the culture of a learned society with global reach and highly efficient and effective publishing systems and processes. With offices in the UK, US, Germany, China and Japan, and staff in many other locations including Mexico and Russia, we serve researchers in the physical and related sciences in all parts of the world.

IOP Publishing is a wholly owned subsidiary of the Institute of Physics. The Institute is a leading scientific society promoting physics and bringing physicists together for the benefit of all. Any profits generated by IOP Publishing are used by the Institute to support science and scientists in both the developed and developing world. Go to

The Institute of Physics

6. The Institute of Physics is a leading scientific society. We are a charitable organisation with a worldwide membership of more than 50,000, working together to advance physics education, research and application. We engage with policymakers and the general public to develop awareness and understanding of the value of physics and, through IOP Publishing, we are world leaders in professional scientific communications. Go to

Michael Bishop | EurekAlert!
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