GIMP, a free software, multi OS image manipulation program that can generate fractal flames.Electric Sheep, a screen saver created by the inventor of fractal flames which renders and displays them with Distributed computing.JWildfire, a multi-platform, open-source fractal flame editor written in Java.Chaotica, a commercial fractal editor which supports flam3, Apophysis and further generalizations.Apophysis, an open source fractal flame editor for Microsoft Windows and Macintosh.Not all Flame implementations use density estimation. The idea is to vary the width of the filter inversely proportional to the number of samples available.Īs a result, areas with few samples and high noise become blurred and smoothed, but areas with many samples and low noise are left unaffected. FLAM3 uses a simplification of the methods presented in *Adaptive Filtering for Progressive Monte Carlo Image Rendering*, a paper presented at WSCG 2000 by Frank Suykens and Yves D. This problem can be solved with adaptive density estimation to increase image quality while keeping render times to a minimum. One does not however want to lose resolution in the parts of the image that receive many samples and so have little noise. The noise that results from this stochastic sampling can be reduced by blurring the image, to get a smoother result in less time. The flame algorithm is like a Monte Carlo simulation, with the flame quality directly proportional to the number of iterations of the simulation. On the below half, rendered with Density Estimation, the noise is smoothed out without destroying the sharp edges.
![ultra fractal vs apophysis ultra fractal vs apophysis](https://wallpaperaccess.com/full/331353.jpg)
![ultra fractal vs apophysis ultra fractal vs apophysis](https://www.saashub.com/images/app/context_images/27/dd4986d79a5b/apophysis-alternatives-medium.png)
In the above half, you can see the noise and individual samples. Density EstimationĪ demonstration of Density Estimation. To increase the quality even more, one can use gamma correction on each individual color channel, but this is a very heavy computation, since the log function is slow.Ī simplified algorithm would be to let the brightness be linearly dependent on the frequency:įinal_pixel_color := color_avg * frequency_avg/frequency_max īut this would make some parts of the fractal lose detail, which is undesirable. This is implemented in for example the Apophysis software. The algorithm above uses gamma correction to make the colors appear brighter. frequency_max is the maximal number of iterations that hit a cell in the histogram.įinal_pixel_color := color_avg * alpha^(1/gamma) //gamma is a value greater than 1. For example, create a histogram with 300×300 cells in order to draw a 100×100 px image each pixel would use a 3×3 group of histogram buckets to calculate its value.įor each pixel (x,y) in the final image, do the following computations:įrequency_avg := average_of_histogram_cells_frequency(x,y) Ĭolor_avg := average_of_histogram_cells_color(x,y) Īlpha := log(frequency_avg) / log(frequency_max) This involves creating a histogram larger than the image so each pixel has multiple data points to pull from. To increase the quality of the image, one can use supersampling to decrease the noise. The colors in the image will therefore reflect what functions were used to get to that part of the image. The color P.c of the point is blended with the color associated with the latest applied function F j:Īfter each iteration, one updates the histogram at the point corresponding to (P.x,P.y). V 1( x, y) = (sin x,sin y) (Sinusoidal).The functions V k are a set of predefined functions.
![ultra fractal vs apophysis ultra fractal vs apophysis](https://azraelmordecai.weebly.com/uploads/1/2/9/3/12932831/186710_orig.jpg)
Set of flame functions: \displaystyle:s are non-negative and sum to one, but implementations such as Apophysis do not impose that restriction.
![ultra fractal vs apophysis ultra fractal vs apophysis](https://img.appnee.com/appnee.com/Apophysis-4.jpg)
First, one iterates a set of functions, starting from a randomly chosen point P = (P.x,P.y,P.c), where the third coordinate indicates the current color of the point.