Some escapetime shape formulas also start with an underscore. Note: the naming and categorization conventions are not necessarily consistent. These formulas are identified by an underscore _ prefix at the beginning of the formula name. An Escapetime Transform won't work on a dIFS shape, and a dIFS transform won't work on an Escapetime formula.įormulas are categorized according to their type: escapetime non-analytic, escapetime analytic, escapetime transform, dIFS shape, and dIFS transform.ģD formulas are escapetime, non-analytic shapes.ģDa formulas are escapetime shapes with analytic DE based on an additional value, the W variable.ĤD formulas are escapetime non-analytic shapes, also using the W variable.ĤDa formulas are escapetime analytic shapes, using another variable for the analytic calculation.Īds formulas are escapetime transforms. Transform formulas are written in Escapetime and dIFS varieties. A transform affects the formula after it, whether that is on the current run of the sequence or the next one. This can make it appear that the Transform formulas' influence is bidirectional, but it is not. A Transform formula placed at the end of the tab sequence can modify the next iteration of the formula placed at the beginning of the tab sequence. With sufficient Iterations, the sequence of formula tabs repeats in a cycle. For this reason, they are sometimes called pre-transform formulas. 1 will apply an effect to the formula in tab No. Transform formulas do not generate any fractal objects, but apply various spatial functions to the associated Escapetime or dIFS formulas.Ī Transform formula is applied to the formula immediately after it.
Note that dIFS formulas are not related to Iterated Function Systems, a method for generating fractals by iterating a formula most commonly seen in flame fractal programs, though some of the escapetime formulas use an escape time version of this (they have "IFS" in their names).īoth escapetime and dIFS shapes can be modified with transform formulas. This results in the shape being repeated at different sizes and locations. Most dIFS formulas have a parameter "Apply scale+add" if it is 1, the values of the Scale, Z add, Y add, and X add parameters are applied to the point when computing successive iterations. iterations value, which should generally be small for dIFS formulas the bailout value is not used. The number of iterations is always the Max. The smallest distance for all the iterations is used as the distance from the point to the shape. Iteration is not used to determine the distance, but the formulas are iterated and a distance computed for each iteration. In contrast to escapetime formulas, dIFS formulas implement shapes by directly computing the distance from a point to the shape. Mixing analytic formulas with non-analytic formulas results in a non-analytic calculation. Analytic DE formulas generally render faster. There are two types of escapetime fractals: analytic and non-analytic. Points that are part of the object (called "inside" points) will not escape at all.Īnalytic and non-analytic escapetime fractals Points that are far from the object will escape quickly, and points that are near the object will take longer to escape. The length of the orbit before escaping is used to estimate the distance from the initial point to the fractal object. The calculation ends when either some point "escapes" by exceeding the bailout value or the orbit length reaches the Max. A formula is iterated by passing the initial point P 0 to the formula, obtaining a new point P 1, then passing P 1 to the formula, obtaining P 2, and so forth. Escapetime is the method for generating Mandelbulbs, Mandelboxes, and other fractal objects. The primary distinction among formula definition types is between escapetime formulas and dIFS formulas. It doesn't use mesh vertices or polygons.Įscapetime fractals Mandelbulb3D uses distance estimation (DE) to optimize calculations of fractal formulas.
The rendering engine in Mandelbulb3D is special and different from traditional scanline and raytrace renderers. Click a formula name to load it into the currently selected Formula tab, over-writing whatever is there.ĭistance estimation Hover the cursor over a button such as 3D or 3Da to see a drop-down list of formulas in that category. The various categories of formulas can be browsed from the buttons directly below the formula tabs. Mandelbulb3D is a hybrid distance estimation renderer that can combine escapetime and IFS shapes in the same scene.
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