The ground group is a group of 5 layers with slightly different coloring that are averaged using a technique proposed by Kerry Mitchell. Layer 2 is a mask for the 2D layer, and layers 3 and 4 are sliced Juliabulb layers for coloring and raytracing. Examine the parameters on both the Formula and outside tabs to see how this is done. The top layer is a 2D layer that provides coloring for the internal Julia fractal.
Look at the cutting plane parameters to see how the slicing is done. The Juliabulb is sliced, which reveals an internal Julia fractal. Much of the complexity is in creating the background. This is a sliced Juliabulb and is the most complex upr of all in the plug-in tutorials.
Open the Formula tab to examine the parameters on the top two layers. In this example the variant is MandelbulbZpXp3. Over 90 variants of the Mandelbulb are available with the Mandelbulb plug-in. The delta DE method, which does not require the analytical derivative of the fractal function, is used for calculating the normals to the surface. This is a two layer image with the bottom layer a raytraced grey scale image. In example 1, its a Mobius shape from a corner of the Mandelbox. With scale = -1.5 many "traditional" fractal shapes can be found on the surface, most of which require extensive zooms. One of the more interesting ones is the scale parameter. There are many parameter options for the Mandelbox. Tom Lowe's Mandelbox, also known as the Amazing Fractal, is the first example. They can be used to slice the 3D fractal to see interior structures. The cutting planes are applied after any rotations. 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 Display type of Iteration has two coloring options: Vepstas and Exponential smoothing.Ĭutting planes. These options are used primarily for coloring and can be combined with raytracing on the same layer. Besides a Display type of Raytrace, the options of Distance, Z value and Iteration are available. A brute force method is also available, but it is MUCH slower. 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.
#MANDELBULB 3D FORMULA TUTORIAL FULL#
The full raytracing mode occurs with Object view set to 3D and Display tpe set to Raytrace. The Z axis rotation is the rotation angle on the Location tab. The 3D fractal can be rotated around the X, Y and Z axes. Each 3D fractal has its own set of parameters. The shadow level is determined by the coloring formula.įractal formula. Decreasing object roughness slightly may reduce the false shadows. 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. Shadows will be calculated if Add shadows is checked. This is available only with a Display type of Raytrace. Infinite light is defined by a rotation and an elevation value. With Point source the origin and point at positions can be anywhere in 3D space. The Light type can Point source or Infinite light. There is also an option to center the camera on the X-Y zoom coodinates. The camera can be positioned anywhere in 3D space.
This includes the Object view (2D or 3D) and the Display type (Raytrace, Distance, Z value or Iteration).Ĭamera settings. Parameter visibility depends upon the main Raytrace parameter selection. More detail can be found in a book titled Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals by Dang, Kauffman and Sandin. The main algorithm is based upon an article by Hart, Sandin and Kauffman for estimating the distance from a point to a fractal surface. The main raytracer has a number of options and parameters. Two coloring formulas are available: 3D Fractal Coloring Gradient Progressive and 3D Fractal Coloring Direct Progressive. This is a 3D raytracing formula with 60 3D plug-in formulas available.