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Failures of the Flameįractal creation is very much analogous to ray-tracing and path-tracing. Once the image is completed, the intensity is converted to brightness by means of a gamma function to make the final image more visually appealing. If and when they do, they too are added to the pixel, increasing the pixel “intensity”. A number of other sample points may fall on the same pixel. The process is then continued via xaos until the sample point has been run through a certain number of transforms, at which time, it has run its course and a new sample point from the starting square is chosen. Once a point has been run through a transform, it is “added” to the final image at its new destination point. The traversal through the table is dictated by relative weights, called “xaos”, which indicate which transforms should come next after the sample point is modified by one of the transforms in the table.
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Each transform has its own set of modification rules that change the spacial coordinates and color of the sample point. The fractal flame algorithm involves taking a sample point from a square in space and tracking it as it is modified by a table of transforms.
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2) and its successor Apophysis 7x were some of the first if not the first software applications to use this algorithm.
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Fractal flames do not always possess fractal-like qualities, but instead have come to refer to the visual output of software that obeys certain fractal or fractal-flame-related algorithms.Ĭommonly, fractal flames are created using the algorithm authored by Scott Draves. When such a repetitious process is used, especially in conjunction with non-iterative techniques, the resulting pseudo-fractal is called a “fractal flame”. It is possible then to create pseudo-fractals by performing this iterative process for a limited number of times until visually it is difficult for the audience to see how the result of this process differs from the complete fractal. Other fractals are created by iterating a simple shape over and over again. The definition of the edge is determined by the granularity of space in such cases. Consequently, fractals have a kind of half-dimension unlike anything else in the world.Īuthentic fractals can be mimicked by real things in life such as clouds, trees, and bacterial colonies, but all of these have definitive edges at a specific zoom level.Ĭertain fractals are visualized by sampling coordinates in space and checking whether or not that set of coordinates is inside or outside the fractal. However, every coordinate in space is either inside or outside of the fractal. No matter how close you zoom in on them, it is impossible to identify the “end”. They have an interior and an exterior but no definitive edge or ending point. What follows in this article is an overview of those thoughts and an analysis of some of the solutions I’ve been dreaming up.įractals are complex shapes.
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Out of disappointment, I’ve pondered the details of the process and how to improve it. However, fractal creation can be inherently slow or spotty in appearance depending on the type of fractal being rendered and the software used. There is an enormous potential in fractal design, and I’d like to see it manifested. The fine details are the main attraction and the source of endless entertainment. It drives you to want to see more and more (and spend hours on end rendering it). On the other hand, the artwork never provides complete gratification. On the one hand, you are creating the most liberal art in the universe – pure color and shape – without so much as a single relation to a controversial topic. After toying with various software and examining their inner mechanisms, I’m now familiar with how each of these programs render fractals.Īddiction to creating fractals can be a blessing and a curse. Not considering CPU vs GPU, there are a couple of common approaches, and I have had the pleasure of trying them all out. Having been creating fractals for a number of years, I have grown considerably interested in making software that allows me to create these structures. This article is more about improvements to the general process in the software for rendering fractal flames. My astute readers may note I have written a more complete description of the actual algorithm for fractal flames in another article.