![]() ![]() How does it look? This animation took about 45 minutes to render at an acceptable quality (with DistanceFactor = 0. ![]() The final magnification of the Mandelbrot fractal is 6.066e+228 (2760) want some perspective 1E6 Vancouver Island. You also want to play this, to make people start bouncing if they’re reluctant somehow. A proper rendering of the fractal (even in 2D with constant $d$) should better take into account the multiple values, but I don't know the best way to do this. Appropriate for later progress in the evening as well as taking it down a notch, whilst sustaining the energy level. This leads to the "cut" that appears along the negative X axis. There is another problem: non-integer powers of complex numbers are multivalued, because complex $\log$ is multi-valued (the imaginary part can have arbitrary integer multiples of $2 \pi$ added to it). Small changes in $d$ might lead to large changes in the distance estimate, but hopefully the change is bounded above by a constant factor. This is to try to mitigate the inherent problem with this approach: the distance estimate is only valid in the plane where the power $d$ is constant, but the ray direction in general has varying $d$. Note the use of the DistanceFactor variable to scale the distance estimate. Return 0.5 * log(r) * r / dr * DistanceFactor You can view additional useful information such as the graph axes and the corresponding Julia set for any point in the picture. Using FragM's DE Raytracer, a "Multibrot Stack" distance estimator can be implemented like this: uniform float Iterations // e.g. Explore the famous Mandelbrot Set fractal with a fast and natural real-time scroll/zoom interface, much like a street map. FragM 2.0.0 has a ag with complex dual numbers for automatic differentiation. Additionally, where possible I will try and include some additional background information on the video. Here you will find a database of the Maths Town fractal videos with additional information included such as location parameters. Syntopia has a blog with a series of posts on Distance Estimated 3D Fractals, applicable within the software Fragmentarium and its updated fork FragM. Maths Town is currently the largest fractal art channel on YouTube. The ray-marching algorithm calculates the distance from a point on the ray (in any direction, not necessarily the ray direction), and steps the ray forward by this amount, thus the ray gets closer and closer to the object (or passes by it and hits the background). The distance estimate tells you, given a point, how far the nearest point in the fractal is. It is possible to render 3D fractals by ray-marching with distance estimators.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |