We all are familiar with the pixels and resolution concepts as used in modern graphics designing and digital imagery. The beauty of the whole concept of pixels and picture resolution is that as the digital cameras become stronger, more powerful and more loaded with advanced imagery features, the zoom level and the detail level of our captured pictures is enhanced and even more comprehensive.
Similarly, looking at the landscapes from up above the ground level, one wonders as to how differed the whole image looks from the actual surface when we are standing on it in reality. But a question rises in oneâ€™s mind immediately that how deep can this phenomenon of zooming and detailing of images go? Well, may be the answer to this mysterious question lies glaringly with a mathematics concept known as â€˜fractalsâ€™.
Fractals â€“ In Association with Mathematical Concepts:
Fractals can be best defined as the geometrical figures, shapes or graphical theme that keep on depicting the same design patterns incessantly (at least to the naked eye) no matter however cavernously you expand them. The repetitive nature of these shapes remains as mystified and perplexing despite trying to solve it to the maximum level of effort. This iteration (or repetition) has helped the mathematicians and graphics designers alike in building up models and images of their liking by following simple replication steps as characterized by fractals. Fractals and their types can vary infinitely and one can create them in umpteen different ways. From a mathematics viewpoint, the concept of numerous trigonometric designs such as parabolas, hyperbolas and various ellipses could be accredited to the concept of fractals to some extent. This mathematical exploration of the notion of fractals has helped the field of digital imagery and modern graphics designing in a magnanimous way. It has also helped the geologists and meteorologists to study the exact design patterns and geographic structuring of our entire galaxy (inclusive of our own planet earth).
Various Categories Of Fractals:
The fractals that were not deemed appropriate to fit into any predefined categories were referred to as non-standardized fractals. Otherwise, each and every shape that qualifies to the criteria of being termed as a fractal has been braced into at least one of the following categories:
- Base-Motif Fractals
- Fractal Canopies
- Star Fractals
- Mandelbrot Sets
- Pythagoras Trees
- Paper-Folding Fractals
- Julia Sets
- Strange Attractors
- IFS Fractals
- Dusts and Clusters
- Peano Curves and
- Plasma Fractals etc.
Each one of the aforementioned fractals has a distinctive design, shape and characteristics that make them distinguishable from the others. However, there is a similarity common in each of the fractal types which is never ending repetitive design pattern.
Fractals are somewhat simplified the complex mathematical calculations that were otherwise reliant on rather unsatisfactory and inexplicable theories. Fractal equations are very much popular in solving several predictable and forecasting computations such as weather forecasts, image designing/enhancing, data summarization and other mathematical designing complications. Another very popular concept that has emerged from the idea of fractal equations is that of Fractal Mountains that use some relatively simpler triangular concepts to create infinite triangles and eventually end up with a desired shape. Once again, in this concept, the idea of infinite subdivisions of the master graphic is adopted to achieve the desirable shapes and figures.
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