What would the often intellectually daunting ideas expressed by theoretical physics look like if you could hold them in your hands?

Theoretical physicist Dr. Tim Evans wanted an answer to that question, so he and a team of scientists at Imperial College London began thinking about how tenets of complex theoretical physics might be wrought into physical objects using a 3D printer.

The study of theoretical physics began at least 2,000 years ago in a Pre-Socratic world. The pillars of modern physics, relativity theory and quantum mechanics, often use theoretical physics, mathematical models and abstractions of physical objects and systems to rationalize, describe and predict natural phenomena where experimentation cannot be done.

Evans' innovation might let students actually touch some of the often opaque theoretical concepts they learn in physics classes.

The researchers used a 3D printer to create their own eight cubic centimeter object which physically represents a mathematical model of how forest fires are started and spread over the course of time. The process took just eight hours and cost just over $20.

Inspired by a visit to the Victoria and Albert Museum in London, Evans came in contact with the first 3D printed object added to their collection and it got him thinking.

Fractal.MGX table by Gernot Oberfell, Jan Wertel and Matthias Bär

"The object was a table inspired by the tree-like structures found in nature," Evans said. "It's 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?"

Calling his new approach "Sculplexity," Evans says these "sculptures of complexity" may one day be used to create works of art based on science.

Evans and his team took a forest fire as the basis for their initial model. Each segment, or 'cell,' of the model represents a tree in one of three states – alive, dead or burning. The scientists applied rules to determine the state that each cell occupied over time and also accounted for each cell's proximity to other cells and their states.

The modified forest fire model

"A 3D printer builds up its object in layers," Evan said. "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 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."

Evans says that his group is also working on projects like attempting to explain heartbeat anomalies by examining simple models which map the activity of each cell in the human heart muscle, and he thinks that sort of event could be visualized using 3D printing as well.

"All we have done is made the first step in terms of 3D printing and mathematical models, Evans says. "We've highlighted the key problems and given at least one way to fix them."