How fractal geometry can help us understand the brain

Macquarie University neuroscientist and Professor of Neurosurgery, Dr Antonio Di Ieva, has published a second edition of his groundbreaking textbook, The Fractal Geometry of the Brain.

The book brings together scientists and clinicians from domains as diverse as neuroscience, neurosurgery, cognitive neuroscience, mathematics, engineering and computer science to advance the study of the human brain.

The first edition, published in 2016, was downloaded more than 100,000 times, sold several thousand hard copies, and has generated hundreds of research citations.

The new 2024 edition comes in at just over 1000 pages – more than 400 pages longer than its predecessor – and represents the work of 100 expert scientists and clinicians including neurosurgeons, neurologists and neuroscientists.

In addition to editing the book, Professor Di Ieva wrote or co-authored 16 of the chapters.

First introduced by mathematician Benoit B Mandelbrot, fractal geometry relates to the repeating patterns found in nature, and can be used to analyse the complexity of many natural objects, including the human brain. It has applications in fields including physics, geology, astronomy, biology, medicine, finance, computer science and art.

Professor Di Ieva was the first scientist to apply this fascinating field to neurosurgery, realising its potential while undertaking his PhD at the University of Vienna on the application of fractal analysis to the study of brain tumours.

“Neurosurgeons can use computational fractal-based tools to analyse imaging in order to quantify the shape and size of brain tumours, improve diseases’ differential diagnoses, and enhance decision making for improved patient treatment,” he says.

“The book provides an encyclopaedic view of the multiple ways the notion of fractal geometry furthers the scientific and clinical understanding of the human brain.

“It is aimed at neuroscientists and medical doctors whether they are working in the lab or the clinic, but it also has translational applications in fields such as cognitive neuroscience.”

The Fractal Geometry of the Brain, ed. Antonio Di Ieva, is published by Springer and is available now in hardcover or electronic format.