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# Mathematical Ideas Fractals Case Study

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Subject Area:Geometry

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Other fractals discovered later include the Julia and Newton fractals. In 1980 Carpenter Loren did a presentation introducing fractals used in the generation and the rendering of landscapes generated by fractures (Boeing, 2016). Several types of data sets exist. Some include: the Mandelbrot, Morphing, Circular Julia and the random fractal, as shown in Table 1. Fractal Type Dataset Fractal Type Dataset Mandelbrot Fractal Morphing Fractal Random Fractal Circular Julia Fractal Figure 1 Fractal Datasets (Boeing, 2016) Examples of fractals found in nature include sea shells (the nautilus, is an example that is most famous of a natural fractal), lightning (the terrifying power by lightning is both beautiful and awesome; the created fractals fascinates in their irregular and arbitrary shape), snowflakes, fern (is an example of a fractal flora), and romanescu (this is good type of broccoli and is specifically a fractal that is symmetrical) (Falconer, 2003).

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Thus, most images that are created in videos are as a result of the formulation of mathematical formulas, variations in color pallets and filters thereby generating unexplored fractal realms that can be used in films and advertisements. Figure 1 The Mandelbrot Set (Gordon, 2000) Applications of Fractals in Film and Media The biggest application of fractals is in the field of computing and computer science. For instance, several image compression schemes in media utilize fractal algorithms that aid in the compression of large graphic files to half or even a quarter of their initial sizes. In addition, graphic designers utilize fractal geometry in the development of textured landscapes as well as other complex images and illusions. Through the use of fractals, it is now possible to generate real “fractal forgeries” in form of images if natural features such as beaches and their actual coastlines, mountain tops and lunar landscapes.

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The images are generated in computers through the use of mathematical formulas. The formulas can be iterated into creating an infinite number of points in space depicted in unique organic patterns (Mandelbrot, 2004). The iterations of the formulas allows variations of formulas, color palettes and filters thereby generating transient and unexplored fractal realms. These images establish vibrant and unique sets of images that dance on the edges of chaos. At present, fractals are applied in computer modelling of irregular shapes and patterns found in nature contributing to the success of computer animation in films and advertisements. Secondly, there is an opportunity for companies that do weddings and other special events. People that have already established interesting photography that is professional could incorporate drones to the stock of their tools. It sounds presentable to provide aerial footage and pictures of anniversaries, weddings and several other special events (Falconer, 2003).

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Thirdly, there is the opportunity for a company who wants to conduct surveillance and reconnaissance services. Drones are useful in taking aerial photography and therefore recommended for civil and military reconnaissance. This shall help in taking campaigns for marketing to higher levels (Boeing, 2016). Challenges in the use of Drones According to Donald (2008), drones have a restricted endurance to flight and capacity of payload. Drones can only fly for about 15-30 minutes before demanding battery recharge, or swapping. Whereas there exists drones that can support payloads of approximately 20 pounds, those that are common are only 5 pounds or even less. Further complicating matters, is that there exists an inverse relationship between the weight of the payload and the endurance of the flight. The primary mandate of the FAA is to regulate large aircraft, which do flights of significant distances at very high altitudes.

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Drones for commercial purposes are small-sized and mostly does short distance flying at comparatively lower elevations. Most significantly, the FAA does succeed through minimization and risk elimination. It is therefore important to accommodate risks, for the drone industry to succeed (Mandelbrot, 2004). Another challenge is that the drone industry is exerting much time and effort in developing a system with comprehensive traffic management. Conclusion In conclusion, mathematicians have been attempting to provide an accurate description of fractals over the past century. However, with advances in computing power and the imaging efficiency of modern computing devices, fractals are gaining popularity especially in the film and printed media industry. This is because, now, fractals can be digitally rendered much quicker and varied to create unique and fascinating features. Consequently, they are gaining popularity in the generation of computer aided surfaces and landscapes as well as pf planetary visuals in films and advertisements.

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Hence, Computer Generated Imagery is the new frontiers and production houses are encouraged to explore this realm. Mathematical Foundations and Applications. Gordon. Introducing Fractal Geometry. Mandelbrot, B. Fractals and Chaos. Thus, the C is contained in the Mandelbrot and is represented as one of the black points in the image.

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