This is a 3D raytracing formula with 60 3D plug-in formulas available. Two coloring formulas are available: 3D Fractal Coloring Gradient Progressive and 3D Fractal Coloring Direct Progressive.
Parameters and Options:
The main raytracer has a number of options and parameters. The main algorithm is based upon an article by Hart, Sandin and Kauffman for estimating the distance from a point to a fractal surface. More detail can be found in a book titled Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals by Dang, Kauffman and Sandin. Parameter visibility depends upon the main Raytrace parameter selection. This includes the Object view (2D or 3D) and the Display type (Raytrace, Distance, Z value or Iteration).
Camera settings. The camera can be positioned anywhere in 3D space. There is also an option to center the camera on the X-Y zoom coodinates.
Illumination. The Light type can Point source or Infinite light. With Point source the origin and point at positions can be anywhere in 3D space. Infinite light is defined by a rotation and an elevation value.
Shadows. This is available only with a Display type of Raytrace. Shadows will be calculated if Add shadows is checked. Increasing 'shadow sensivity' will give shadows that show less fractal detail, but can also increase the number of false shadows from roughness on the fractal surface. Decreasing object roughness slightly may reduce the false shadows. The shadow level is determined by the coloring formula.
Fractal formula. This is the plug-in for the 3D fractal. Each 3D fractal has its own set of parameters.
Rotations. The 3D fractal can be rotated around the X, Y and Z axes. The Z axis rotation is the rotation angle on the Location tab.
Raytrace parameters. The full raytracing mode occurs with Object view set to 3D and Display tpe set to Raytrace. The two recommended raytracing methods are delta DE which does not require the analytical derivative of the 3D fractal function and iteration smoothing which needs the analytical derivative and uses exponential smoothing for the potential. A brute force method is also available, but it is MUCH slower. Besides a Display type of Raytrace, the options of Distance, Z value and Iteration are available. These options are used primarily for coloring and can be combined with raytracing on the same layer. The Display type of Iteration has two coloring options: Vepstas and Exponential smoothing.
Cutting planes. The starting and ending planes are defined by the X, Y and Z values referenced to the camera position and the plane of the screen. The cutting planes are applied after any rotations. They can be used to slice the 3D fractal to see interior structures.
Example 1:
Tom Lowe's Mandelbox, also known as the Amazing Fractal, is the first example. There are many parameter options for the Mandelbox. One of the more interesting ones is the scale parameter. With scale = -1.5 many "traditional" fractal shapes can be found on the surface, most of which require extensive zooms. In example 1, its a Mobius shape from a corner of the Mandelbox. This is a two layer image with the bottom layer a raytraced grey scale image. The delta DE method, which does not require the analytical derivative of the fractal function, is used for calculating the normals to the surface.
Example 2:
Over 90 variants of the Mandelbulb are available with the Mandelbulb plug-in. In this example the variant is MandelbulbZpXp3. The bottom layer is a background layer. Open the Formula tab to examine the parameters on the top two layers.
Example 3:
This is a sliced Juliabulb and is the most complex upr of all in the plug-in tutorials. Much of the complexity is in creating the background. The top 4 layers are Juliabulb layers. The Juliabulb is sliced, which reveals an internal Julia fractal. Look at the cutting plane parameters to see how the slicing is done. The top layer is a 2D layer that provides coloring for the internal Julia fractal. Examine the parameters on both the Formula and outside tabs to see how this is done. Layer 2 is a mask for the 2D layer, and layers 3 and 4 are sliced Juliabulb layers for coloring and raytracing. Layer 5 is a color filter. The ground group is a group of 5 layers with slightly different coloring that are averaged using a technique proposed by Kerry Mitchell. Notice that the merge mode is Normal for all 5 layers but that the opacity is increased from 20% to 100% through the series. After you have completed the Image Traps plug-in tutorial (still in progress at this point) you may want to come back and look at the details for these 5 layers. The entire ground group has a blend mask which provides the distant horizon between the ground and the sky. The blend mask is followed by a top clouds layer using Worley Textures and a sun layer using Image Traps. The Sky group is the final group with 6 layers using the same averaging technique as for the Ground group. Look at the Formula and Outside settings to see how this is done.
This is a 3D raytracing formula with 60 3D plug-in formulas available. Two coloring formulas are available: 3D Fractal Coloring Gradient Progressive and 3D Fractal Coloring Direct Progressive.
**Parameters and Options:**
The main raytracer has a number of options and parameters. The main algorithm is based upon an article by Hart, Sandin and Kauffman for estimating the distance from a point to a fractal surface. More detail can be found in a book titled Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals by Dang, Kauffman and Sandin. Parameter visibility depends upon the main Raytrace parameter selection. This includes the Object view (2D or 3D) and the Display type (Raytrace, Distance, Z value or Iteration).
**Camera settings.** The camera can be positioned anywhere in 3D space. There is also an option to center the camera on the X-Y zoom coodinates.
**Illumination.** The Light type can Point source or Infinite light. With Point source the origin and point at positions can be anywhere in 3D space. Infinite light is defined by a rotation and an elevation value.
**Shadows.** This is available only with a Display type of Raytrace. Shadows will be calculated if Add shadows is checked. Increasing 'shadow sensivity' will give shadows that show less fractal detail, but can also increase the number of false shadows from roughness on the fractal surface. Decreasing object roughness slightly may reduce the false shadows. The shadow level is determined by the coloring formula.
**Fractal formula.** This is the plug-in for the 3D fractal. Each 3D fractal has its own set of parameters.
**Rotations.** The 3D fractal can be rotated around the X, Y and Z axes. The Z axis rotation is the rotation angle on the Location tab.
**Raytrace parameters.** The full raytracing mode occurs with Object view set to 3D and Display tpe set to Raytrace. The two recommended raytracing methods are delta DE which does not require the analytical derivative of the 3D fractal function and iteration smoothing which needs the analytical derivative and uses exponential smoothing for the potential. A brute force method is also available, but it is MUCH slower. Besides a Display type of Raytrace, the options of Distance, Z value and Iteration are available. These options are used primarily for coloring and can be combined with raytracing on the same layer. The Display type of Iteration has two coloring options: Vepstas and Exponential smoothing.
**Cutting planes.** The starting and ending planes are defined by the X, Y and Z values referenced to the camera position and the plane of the screen. The cutting planes are applied after any rotations. They can be used to slice the 3D fractal to see interior structures.
**Example 1:**
Tom Lowe's Mandelbox, also known as the Amazing Fractal, is the first example. There are many parameter options for the Mandelbox. One of the more interesting ones is the scale parameter. With scale = -1.5 many "traditional" fractal shapes can be found on the surface, most of which require extensive zooms. In example 1, its a Mobius shape from a corner of the Mandelbox. This is a two layer image with the bottom layer a raytraced grey scale image. The delta DE method, which does not require the analytical derivative of the fractal function, is used for calculating the normals to the surface.
**Example 2:**
Over 90 variants of the Mandelbulb are available with the Mandelbulb plug-in. In this example the variant is MandelbulbZpXp3. The bottom layer is a background layer. Open the Formula tab to examine the parameters on the top two layers.
**Example 3:**
This is a sliced Juliabulb and is the most complex upr of all in the plug-in tutorials. Much of the complexity is in creating the background. The top 4 layers are Juliabulb layers. The Juliabulb is sliced, which reveals an internal Julia fractal. Look at the cutting plane parameters to see how the slicing is done. The top layer is a 2D layer that provides coloring for the internal Julia fractal. Examine the parameters on both the Formula and outside tabs to see how this is done. Layer 2 is a mask for the 2D layer, and layers 3 and 4 are sliced Juliabulb layers for coloring and raytracing. Layer 5 is a color filter. The ground group is a group of 5 layers with slightly different coloring that are averaged using a technique proposed by Kerry Mitchell. Notice that the merge mode is Normal for all 5 layers but that the opacity is increased from 20% to 100% through the series. After you have completed the Image Traps plug-in tutorial (still in progress at this point) you may want to come back and look at the details for these 5 layers. The entire ground group has a blend mask which provides the distant horizon between the ground and the sky. The blend mask is followed by a top clouds layer using Worley Textures and a sun layer using Image Traps. The Sky group is the final group with 6 layers using the same averaging technique as for the Ground group. Look at the Formula and Outside settings to see how this is done.
