Mandelbulb3D/Reference/Formulas/Formula hybrids

Formula Hybrids
The formulas loaded into Formula tabs can be combined in three different hybrid modes: Alternate, Interpolate, and DEcombinate.

Alternate
In the default Alternate mode, each formula is alternated with the previous formula. For dIFS formulas, this simply means adding all of the shapes together. For escapetime formulas, Alternate produces a complex layering effect where each formula adds detail to the one before it.

Interpolate
Interpolate mode finds the average of two formulas. Only two formulas are permitted. Both formulas are calculated for each iteration and the results are averaged. The amount of each formula's contribution is adjusted with the Weight attribute near the bottom of the Formula window.

Interpolate only works with escapetime formulas, not dIFS.

DEcombinate
DEcombinate mode performs complex volumetric operations on sequences of formulas. Most of them are what computer graphics applications generally call Boolean modeling operations. Shapes can be added, joined, subtracted and intersected to form new shapes. At its most basic level of operation, DEcombinate mode allows simultaneous rendering of two different fractal objects, such as a bulb and a heightmap. More advanced applications allow carving and sculpting fractals in exciting and creative ways.

Hybrid Part 1 and 2
The key to using DECombinate is understanding that it combines two sequences of formulas. The six formula tabs are divided into two sequences: Hybrid Part 1 and Hybrid Part 2. The breakpoint between these two sequences is set with an unlabeled number field next to the DEcombinate button. This field sets the Formula tab where Hybrid 2 starts. The field only appears when DEcombinate mode is active.

If Hybrid 2 starts at the default position of formula tab 2, then formula 1 is combined with the sequence of formula tabs 2 through 6.

If Hybrid 2 starts at formula tab 4, then the sequence of formulas 1 through 3 is combined with the sequence of formulas 4 through 6.

The maximum number of Iterations for each Hybrid sequence is set with the fields at the bottom of the Formula window. These fields are labeled Maxits hybrid part 1 and Maxits hybrid part 2.

DEcombinate operations
DECombinate has six modes, selected from the pulldown list labeled DE comb. The first five modes correspond to traditional Boolean and parametric modeling operations.

Min
DEcombinate Min mode finds the union of two hybrid sequences. A shape is generated in the volume occupied by either Hybrid 1 OR Hybrid 2.

Max
DEcombinate Max mode finds the intersection of two hybrid sequences. Intersection is the overlapping volume. A shape is generated in the volume occupied by both Hybrid 1 AND Hybrid 2.

Inv Max
DEcombinate Inv Max mode subtracts Hybrid 1 from Hybrid 2. A shape is generated in the volume occupied by Hybrid 2 AND NOT Hybrid 1.

Min Lin
DEcombinate Min Lin mode finds the union of two hybrid sequences and joins their shapes with a straight, linear chamfer. The Ds numeric field sets the width of the chamfer.

Min nLin
DEcombinate Min nLin mode finds the union of two hybrid sequences and joins their shapes with a curved, nonlinear fillet. The Ds numeric field sets the width of the fillet.

Mix
DEcombinate Mix mode combines two formulas in a complex manner unlike any simple Boolean operation. It instances the second formula along the Z vector of first formula.

The Fpow numeric field scales the value of the first formula, affecting Distance Estimation accuracy.

The Co numeric field chooses a color mode. 0 averages the colors of the two formulas. 1 uses the color of the first formula, 2 uses the color of the second formula.