3D Fractal Raytracing Tutorial

 

 

This tutorial is for Ultrafractal 5 and the use of the 3D Fractal Raytrace ufm in reb5.ufm, together with its companion coloring formula 3D Fractal Coloring Direct, which is in reb5.ucl.  The raytracer has the following features:

The coloring formula (3D Fractal Coloring Direct) has the following features:

General Background

Raytracing is a process to provide realistic lighting, perspective and hidden surface removal effects to a scene. A raytracer includes includes a camera (or eye) and one or more light sources. The raytrace process can be envisioned as the shooting of rays from the camera to the objects in the scene. The raytracer uses the distance to the intersection point, the surface normal at the intersection point, and the angle and intensity of the light source(s) to determine the coloring at the intersection point. Precise mathematical formulas exist for calculating these parameters for regular solids such as spheres, planes, cubes, etc. To deal with a general curved surface, the general approach of Hart, Sandin and Kauffman in which the distance to the surface is estimated using calculations from the potential and gradient of the fractal as the surface is approached is used. Calculation of the gradient normally requires the derivative of the fractal function. An alternate method for estimating the gradient is also available. A "brute force" method in which small steps are made until the surface is crossed. Surface lighting of the fractal requires surface normals, which are estimated from four neighboring surface points.

The User Interface

To use the raytracer, select 3D Fractal Raytrace ufm in reb5.ufm  from the Formula tab in UF5 and on the Outside tab in UF5 select 3D Fractal Coloring Direct, which is in reb5.ucl. With the default settings the user should see the following:

Formula tab

 

Outside tab

 

With the default settings the user will see a Phong shaded image for a Julia quaternion.

In the fractal formula, closeness determines how closely the distance to the surface of the fractal is calculated. Greater detail will be seen as the closeness is decreased, but the rendering time will also increase. The number of iterations does not determine how closely the surface is approached. The closeness autocorrects for screen size and zoom.

Some Formula Options

The next image is produced by checking the "Add shadows",  the "Add floor" checkbox and making changes to Illumination and Rotations. These options will not work unless 3D Fractal Coloring Direct is the coloring formula. This will be true for all of the formula options presented here. Here are the changed parameter settings:

Here is the resultant image and the upr for the image:

LightShadowfloor {
::iKMPlin2Vu1WzttNW43zM5/gG9ecw9LdH+SS2uT70uT32s7raolosoDFpKFdsd/1vHAQSrL0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}

The next image and upr are for an 8th power Mandelbulb. Here are the plugin parameters:

8thPowerMandelbulb {
::1o38fhn2Vu12yttRS03dV+fgle3Kz9LZL+Ss3sV2a9WZT8uvyCiEUE2gAMgQWS5rf7ZaAKeB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}

Coordinating the Formula and the Coloring

The distance and 2D options require require changes to the parameters for the coloring. The next image and upr is an example of distance coloring of a hypercomplex julia. The user should examine the parameters for both the fractal formula and the coloring formula to see how the image is created. Notice that the coloring formula uses a gradient rather than a two color preset.

JuliaHyperComplex {
::ebgpejn2VuVWzttRS43dV+/AL+eUm7jsFeJ2bymUJblNx7+qKISQRYDCwACZJlf9bPHAiHQ6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}

Slicing into a 3D/4D object can give some interesting results. The next example is a slice into a Julia quaternion. The top layer uses the 2D mode, the middle layer uses the Distance mode, and the bottom layer uses the Raytrace (Phong) mode. Examine each layer carefully to see the settings for the fractal formula and the coloring formula for each layer.

InsideJulia {
::lAdP4jn2t31SvRuxR47Gw/HGM3tc/+hDmL2bcgDsDSs3krCUzwRD3lD5YOUrk8v+UdXNpmHU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}

The next example, IncaMask, is a two layer image using the Ikenaga Power Juliabulb formula, with a power value of 5. The top layer uses the Distance coloring mode and and bottom layer uses the Raytrace (Phong) mode with shadows The user should examine the parameter settings for the fractal formula and the coloring formula on both layers.

IncaMask_Color {
::OpAxcjn2tz1SzttRS47uK/fgFvb559jsFuY7Nb5tS2Kbi39qKISQRYDCwACaJlf9bPTPAiPg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}

Some Advanced Techniques

Mandelbulbs

Mandelflowers, which is an image of an 8th power Mandelbulb, has four layers and a mask layer. The top layer is a Distance mode layer and provides the colors for the flowers. The next layer is a Raytrace (Phong) layer with shadows and a partially transparent floor which allows the Terra Firma layer to be seen and still maintain the shadow of the of Mandelbulb on the floor. The Terra Firma layer has a fuzzy mask applied to allow the sky layer to be seen and to provide a distant horizon. The user should examine the parameters on all layers in detail to see how the image is created.

MandelFlowers {
::wiSXLhn2t3VWPSuRy53Fg+PUofyGGqm8+QG8FpxjxaoZX5dmd9buB7qY1FnmFJFJ7r5XvjMD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}

Hypercomplex Objects

This example is a Sci-Fi style image that takes a different approach with the coloring formula in that both the Distance and Raytrace layers are colored using a gradient. The fractal is a Hypercomplex Julia object. The user should examine the parameters on all layers in detail to see how the image is created.

Decompression {
::cqwHxin2t31STutxR47qK9fgFvEnDiae/wpwFrNyxusSlYJnrbhlEcJkABoBwqdX/rP9MNAW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}

Juliabrots

Phoenix Landing, which features a phoenix juliabrot, is the most complex image in the tutorial, and features several formulas besides 3D Fractal Raytrace and 3DFractal Coloring Direct. It is comprised of 7 layers and 2 masking layers. Two of the layers (Phoenix Top and Landing) use the 2D mode of  3D Fractal Raytrace. Unlike the previous example with the 2D mode, 3D Fractal Coloring Direct is NOT used. This requires that the compatibility check box be unchecked in 3D Fractal Raytrace. Another 3D fractal type is introduced which uses a pixel formula for the fractal formula and Landscape for the coloring formula. It is used for the mountains. The user should examine the parameters on all layers in detail to see how the image is created.

NewPhoenixLanding {
::Zzzbdin2szTSzutRzdXVp/Ds4pkD6pZfxp4hYJ7UKllrvY74c8V4RA+IkABgBwbz/6TPLAEk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}