Cinema 4d fractals4/4/2023 ![]() You can clearly see the artifact of how the algorithm works in the rings in the image to the left (each ring is a sample point along the ray). The left image has a higher distance between sample points compared to the image to the right. The process of sampling each point can be very time consuming so the distance between sample points can not be to small, but it can not be the to high either as it directly relates to the point resolution you get as exemplified by these two images: Here is 2D illustration of how a ray is thrown and sampled at regular intervals: ![]() The algorithm traverse these vectors step by step (from the camera) and for each point the Julia equation is recursively run to determine if the point is part of the Julia set or not. What is needed is a 4D camera from which you can cast rays (vectors). It becomes a lot trickier to visualize however. ![]() When using the Julia equation with Quaternions we can define a 4D dimensional object. These are called Quaternions and can be visualized as a four dimensional space. A complex number is a tuple of two values, a real and imaginary part, which can be visualized in the complex pane, which is a 2D geometric representation of complex numbers.Ĭomplex numbers can be extended to a four-tuple value with one real and three imaginary units. The variable z and constant c are in a normal 2D Julia set complex numbers. The simple formula that defines the Julia and Mandelbrot set is also something that many know: The 2D Julia fractal to the left is a shape that everyone recognizes. This generated a quite serious outcome during a course on research methodologies where I together with a friend wrote a scientific paper on 4D Julia rendering. I did a lot of hobby programming with games, like the Quake 3 mod Rocket Arena 3, and specifically with fractal graphics. My main area of interest in programming during my school and university years was in computer graphics.
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