WhatisthelengthofBritain’scoastline?Howdoesafrostcrystalgrow?Howmanyquestionsarethereintheproblemset?Findingananswertoeachoftheserequiressomeexplorationoffractals.
Afractalisarecursivelycreatednever-endingpatternthatisusuallyself-similarinnature.SeparatefromEuclideangeometry,fractalgeometryaddressesthemorenon-uniformshapesfoundinnature,suchasmountains,cloudsandtrees.
Fractalsprovideasystematicmethodtocapturethe“roughness”ofsomeobjects.Thismethodtocaptureroughnesshasusesinawidevarietyoffieldsrangingfromprogrammingtomedicine.
HereintheFacultyofMathematics,studentsandresearchersareactivelyworkingonfractalgeometry.CheckoutresearcherslikeWilliamGilbert,professoremeritusintheDepartmentofPureMathematics,andtheWaterlooFractalCodingandAnalysisGroup.
Joinusasweexplorethetopfiveapplicationsoffractals.
- Fractal cities. Some cities tend to grow in fractal patterns over time and are called fractal cities. As a large fractal city absorbs its neighbouring towns and villages, the pattern developed resembles a self-similar structure that seems random at first but is a dynamic network that may prove to be more efficient than modern “pre-planned” cities.
- Fractal medicine. Knowledge of fractals is especially useful in medical diagnoses, including for cancer. Since healthy human blood vessel cells typically grow in an orderly fractal pattern, cancerous cells, which grow in an abnormal fashion, become easier to detect. This form of fractal analysis makes distinguishing between healthy cells and signs of concern much easier.
- Image compression and resolution. Since fractals allow us to convey seemingly random patterns with little data, working with image resolution and even 3D model creation becomes hugely data-efficient using fractal image coding (FIC) and other applications.
- Antennas. The typically self-similar nature of fractals is also helpful in creating and operating antennas. Curves like the Hilbert curve can be used to design high-performance and low-profile antennas. When they are combined with EM radiation concepts, multi-band antennas can also be operated. Read more here.
- Art. The simplistic to the complex range of rules that govern fractal creation are downright alluring for artists. For example, the Mandelbrot set is well known for providing different “scenes” based on the colour scheme used for its display.
BytheNumbersisaweeklyseriesthatreflectsonthelightersideofstudentlife,research,andinnovationintheFacultyofMathematicsattheUniversityofWaterloo.Staytunedtothisspaceforthenextinstalment.
