Fractals and Fearless Predictions

What is it about man’s fascination with predicting the future? Can man really predict earthquakes and volcanic eruptions? A JCU scientist believes we can.

by Anastasia Koninina

Halfway around the world from Australia, German football fans watched eagerly as Paul, the octopus, ever so slowly made a choice between two competing teams vying for the 2010 FIFA World Football Cup. Seven times out of seven, Paul correctly predicted the winner of each of the German national football team’s matches in the World Cup, as well as the outcome of the final between Spain and the Netherlands. Spain won.

Somewhere in India, a 13-year-old high school student is busy observing a cockroach sitting placidly under a glass dome. As he observes, he pulls a string tied to a rough, red brick across a plank to make the table vibrate. Soon, the cockroach begins running around as the tabletop starts shaking. The student’s experiment hopes to show that insects such as the cockroach can sense small tremors in the ground that are the usual precursors of an earthquake.

In 2009, an Italian scientist made a bold prediction that a destructive earthquake would hit central Italy. His announced date came and went with no result and many accused him of spreading panic. However, less than a week later, a magnitude 6.3 earthquake did strike in the Abruzzo region sparking renewed interest in his earlier claim. His method? He had been measuring spikes in radon gas in the area.

Radon is a radioactive, colourless noble gas that is formed as part of the normal decay chain of uranium and thorium. His theory goes that before a major earthquake, the fault line adjusts itself and, during this process, the gases are released.

Structural and Economic Geology Professor Dr Tom Blenkinsop  had always been interested in rocks and fossils as a child. Growing up in the UK, he recalled accompanying his grandfather to collect fossils in Dorset t age seven.

 

His own interest in geology and fractals was inspired by a teacher who told him that fractals would become a new movement. Professor Blenkinsop said he believes his study of fractals might lead him to the prediction of natural events such as volcanic eruptions and earthquakes.

So what are fractals? In 1975, French-American mathematician Benoit Mandelbrot coined the term fractal from the Latin adjective, fractus, to denote anything that is like a broken-up stone—irregular and fragmented.

Mandelbrot’s study focused on the occurrence of many ‘rough’ phenomena in the real world such as mountains, coastlines and river ways that he said were, far from unnatural, actually quite intuitive and natural.

Professor Blenkinsop met Professor Mandelbrot in Munich shortly before Mandelbrot’s death in 2010.

“I was organising a conference on fractals that occurs roughly every four years. It was not a big conference; probably around 70 or 80 people. That’s what he enjoyed. He could talk to each person individually.”

Professor Blenkinsop said Mandelbrot gave him useful advice at that meeting, which inspired him to continue with his work.

“Fractals are evident not only in mineral deposits but also in a whole variety of phenomena such as volcanoes, earthquakes and faults in the earth’s crust.

“I rapidly discovered that fractals were in an amazing amount of geological phenomenon and how mineral deposits follow fractal distributions,” he said.

“Fractals encapsulate self-similarity: when we look at an object that consists of small and large parts – it looks similar at different scales.”

Examples of fractals might include the humble broccoli with its compound structure of small segments that resemble the whole piece, or seashells with chambers, starting from the small size in the centre and continuing with segments of a larger size to its outer edges.

“In a group of objects, there are often many more small objects than large ones, and the ratio between them is given by a number called the fractal dimension,” Professor Blenkinsop said.

He said fractal patterns are usually found in the way rivers, rocks and mineral deposits are constructed.

“Floods and rivers tend to follow fractal distributions. These patterns are used to estimate the occurrence of floods occurring in that river, which is a very important information if you live in a flood-prone area.”

However, the list of fractals in nature is not limited to these features. Earthquakes and volcanoes tend to follow the same distributions.

“Fractal distributions of earthquakes are very important, because knowing the relationship between the numbers of small and large events with some degree of confidence, we can say that there will be so many earthquakes of a certain size in a certain region over a certain period of time.”

Despite the fact that it is evident that earthquakes follow the same fractal distributions, the JCU scientist said the current knowledge of fractals would not be sufficient to predict the precise time and location of earthquakes at this stage.

“That’s more difficult. Ideally, an earthquake prediction would show when and where an earthquake will occur and how big it is going to be,” Professor Blenkinsop said.

“What we can do and might do is to estimate the number of earthquakes that might occur within a certain period of time at a certain place.

“We are not able to understand the process of earthquakes enough in order to be able to make these predictions.”

Another example of fractals can be seen in the construction of the World Wide Web.

Fractals, with their compound structure of particles of similar appearance, are being used by artists to produce compound images.

“To me, fractal art involves a great effect and great subtlety, and perhaps more creativity.

“I think fractal art is a creative and expressive activity. It is not simple or random, I think it is not anyone of us can do.”

Digital artist and former JCU student Rob Donaldson creates images that showcase his fascination with fractals.

On his website, Donaldson said he finds this method brings the “happy accidents” into his pieces.

He specialises in digital images and uses fractals and other randomly generated structures to give a “nature of chaos” to his works.

For the future, Professor Blenkinsop hopes his research will prove fractals can help find new mineral deposits as well as possibly predict natural disasters.

He gamely predicts there will be more scientific as well as popular interest in fractals.

“It is a very good time to be involved in this research because lots of people have realised that it is a new and exciting field. So there is a lot of encouragement from people to pursue this line of research and lots of things to find out.”