One reason for the popularity of this design element might be research that shows fractal patterns are visually pleasing and even stress-reducing. Within larger fractals, you can almost zoom in and find even smaller pieces of art.įractals can be the basis for beautiful background patterns or single art elements for design projects. They may have a geometric shape – or contain many shapes therein – or have irregular curves and shapes without symmetry. Most fractal art elements are abstract elements that have an obviously digitally-created look and style. Modern fractal art is created with an algorithm and calculations that create a result that might be a still image, animation, or other type of moving media. (Which isn’t that far off from the old-school model when you consider the relationship between math and algorithms.) While fractals can be an element of nature, mathematical formula, or hand-created, the more modern definition of fractal art extends to images and elements that are digitally created using an algorithm. Many of these patterns and shapes mimic things that might exist in nature, such as the nautilus (nature) as it pertains to the Fibonacci sequence (mathematical).Īnother example of a historical fractal is a mandala. By definition, a fractal element is a geometric pattern that is repeated with smaller and/or larger scales to create irregular shapes and patterns. Stay tuned to this space for the next instalment.A fractal is rooted in mathematics and geometry plus visual design. For example, the Mandelbrot set is well known for providing different “scenes” based on the colour scheme used for its display.īy the Numbers is a weekly series that reflects on the lighter side of student life, research, and innovation in the Faculty of Mathematics at the University of Waterloo. The simplistic to the complex range of rules that govern fractal creation are downright alluring for artists. When they are combined with EM radiation concepts, multi-band antennas can also be operated. Curves like the Hilbert curve can be used to design high-performance and low-profile antennas. The typically self-similar nature of fractals is also helpful in creating and operating antennas. 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. This form of fractal analysis makes distinguishing between healthy cells and signs of concern much easier. 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. Knowledge of fractals is especially useful in medical diagnoses, including for cancer. 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. Some cities tend to grow in fractal patterns over time and are called fractal cities. Join us as we explore the top five applications of fractals. Check out researchers like William Gilbert, professor emeritus in the Department of Pure Mathematics, and the Waterloo Fractal Coding and Analysis Group. Here in the Faculty of Mathematics, students and researchers are actively working on fractal geometry. This method to capture roughness has uses in a wide variety of fields ranging from programming to medicine. Separate from Euclidean geometry, fractal geometry addresses the more non-uniform shapes found in nature, such as mountains, clouds and trees.įractals provide a systematic method to capture the “roughness” of some objects. Watch video on YouTube What is the length of Britain’s coastline? How does a frost crystal grow? How many questions are there in the problem set? Finding an answer to each of these requires some exploration of fractals.Ī fractal is a recursively created never-ending pattern that is usually self-similar in nature.
0 Comments
Leave a Reply. |