Four different 3D renditions of the Phoenix fractal

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Here are 4 different 3D Fractal images, all created with Ultrafractal 5. The image theme is centered around the Phoenix fractal discovered by Shigehiro Ushiki. All of the images have the x-y plane (the traditional complex plane) tilted at 60 degrees. The first two images are sliced at z = 0.

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The first image is a standard quaternion for the Phoenix fractal.

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The second image uses the standard mandelbulb algorithm.

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The third image is a Juliabrot using the Phoenix fractal.

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The fourth image and last image is a heightfield created from a 3D triangular mesh of heightfield values (x,y,z) where x and y are the complex coordinates of the fractal and z is the height value. Height values can be regular iteration values or a variety of smoothed iteration values. Orbit trapping can also be used. There is NO distance estimation in the raytracing. The ray distance is the distance to the closest triangle in the mesh, and so is considerably more accurate for surface determination than any distance estimate method. The sides should not be some nice shiny smooth surface but should show the fractal detail as determined by the iteration values. The surface normals are calculated using the Phong triangle method with barycentric coordinates.

For the image  the triangular mesh contains 105,000 triangles and the height values are the simple iteration values with a maximum iteration 0f 100. For iteration values near zero the image fades to transparent so that the heighfield fractal appears to float.