In the late 1980s, Chaos Theory came to the fore in the realm of science popularisation. Strange attractors and the so-called butterfly effect became a part of modern culture. The science was often lost in the wake of beautiful artful representations of the mathematics in the form of colourful fractals that were generated on the computer and revealed the spiralling infinities within. Terms such as the Julia set and the Mandelbrot were scattered around as butterfly wings on the breeze.
Of course, the public fascination may have dwindled as the next trendy discovery came along, but scientists keep working on such things, following the threads that might lead to a new discovery within the coils of those fractals. Now, writing in the International Journal of Advanced Intelligence Paradigms, a team reports how they have used Julia sets and a logistic map to devise a new way to compress and encrypt digital information based on fractals.
Bhagwati Prasad and Kunti Mishra of the Department of Mathematics, at Jaypee Institute of Information Technology, in Noida, India, suggest that their success with their proposal could open up a new efficient and secure way to send confidential images, such as those from medical imaging, military, and other multimedia applications.
The team has demonstrated proof of principle with their approach using various medical images, including a conventional chest X-ray, an MRI (magnetic resonance imaging) scan, and a CT (computerised tomography) scan. For these images they were able to compress and encrypt the files by almost ten times.
Prasad, B. and Mishra, K. (2019) ‘A novel encryption compression scheme using Julia sets‘, Int. J. Advanced Intelligence Paradigms, Vol. 13, Nos. 1/2, pp.8-14.