Xaos and Linked Transforms | Fractal Architect

What is Xaos?

Xaos (also called Chaos Weighting) is a modification of the original Flame Fractal algorithm. The affect of Xaos on the fractal image is small.
Linked Transform (discussed below) can have a major impact on the fractal image.

After each transform iteration of the Flame algorithm, a Xaos From/To conditional weight is pre-multiplied to the each Transform's weight probability.
Every transform has a unique Xaos FROM / TO weight value for all transforms. These weights range in value from 0.0 to 1.0 (0% to 100%).

OK, lets ignore what the Xaos weights do, and just understand that they are new parameters for tweaking that may (or may not) improve the fractal's appearance. Trial and error is the user rule here. And the app makes it easy to do.

This is the original fractal with default 100% Xaos weights for every transform.

Effect of Random Xaos Weights

After opening the Variants editor on that fractal, the Xaos randomization option was selected.

This picture shows a bit of 4 different Xaos variations.
For this fractal, the random Xaos settings affect the color intensity of the gray and gold rings.

Every fractal is different. It is so easy to use the Variants editor to try different Xaos combinations.

Triangle Editor

In the Triangle editor, each transform's From/To Xaos weights are fully editable.

Variants Editor

One of the Variant types is Xaos. Select the Xaos tab to randomize the Xaos weights amongst the created variants.

Random Fractal Generator

Check the Random Xaos checkbox and the created fractals will have random Xaos values.

What are Linked Transforms?

Linked transforms are special Xaos weights of 1. (or 100%) from one transform to another transform. They enable new shape combinations that transform weights alone can not accomplish.

During a fractal's rendering the two transforms are "linked together". When the rendering algorithm chooses and processes the first transform of a linked pair, the next iteration will ONLY choose the linked transform to process.

The affect of Linked transforms is to create new shape combinations that normal usage of transform weights would not achieve. Linked transforms have a moderate affect on the fractal appearance.

Random Fractal Generator

You can tell the fractal generator to add linked transforms to each random fractal. Just set the + Linked count field to a number greater than zero.

Triangle Editor

There are two different ways to add Linked Transforms:

Select a transform then click either the + Linked or the + Back Linked button to link a new transform to the selected one.
Manually edit the Xaos weights to create a linked pair of transforms by hand.