Release 4.0

Attractor - Formula Parameters

The formula tab lets you specify the transformation formulas to use for the fractal.

• Iter [M]

  Specifies the number of iterations to perform. The value is specified in millions. In order to have a nice looking object you need quite many pixels.

• Formula

  Contains the formula sets which are defined for this fractal. ChaosPro will randomly select one of them, apply the formula set to z and draw the pixel. It then will again randomly select one of them, apply it, and draw the pixel. This is the rendering algorithm.

  The buttons at the right side let you add a new formula set to the list and let you delete the current formula set. As there must be at least one formula set, you cannot delete the last one.

  The small arrow at the right side of the button which lets you add/define presets, pre-defined formulas with proper parameters.

• Weight

  This property specifies how often this formula set is selected compared to the other formula sets.

• Color

  You can assign a color to a formula set. The coloring formula may (or may not) use this color in order to calculate a color for a pixel. If the coloring formula does not use this property, setting it has no effect.

• Hide

  By checking this item you can temporarily disable the complete formula set. It has the same effect as deleting it. But by using this check box you can switch it on again if you like without having to assign the formula again and perhaps entering dotzends of parameters again.

   

• Search

  The large slider below and the button at the right side let you search for new parameters: As it sometimes is quite difficult to find new parameters which produce a nice image ChaosPro can randomly select parameters, check whether the resulting attractor is "reasonable", if yes, render the resulting fractal, if not, randomly select again, until reasonable parameters are found.

  The feature does not work with all formulas: A transformation formula must support this feature by declaring which parameters can be randomly chosen. In order to decide whether the resulting fractal is "reasonable", ChaosPro calculates an approximation of the Lyapunov exponent: If this exponent is too large, the system is expansive, i.e. cannot be rendered, as the pixels go to infinity. If the exponent is too small, the resulting object is too contractive, i.e. only consists of single points and lines.

  The slider itself lets you specify the range within to randomize the parameters: Default is 100%, i.e. parameter values are randomly chosen from the complete allowable range. If you set it to 1%, then the parameters are only slightly changed, i.e. around current value +/- 1% of random range, thus slightly modifying the current object in a random manner.

After the Search controls the different formulas contained in the current formula set are displayed and can be modified: You can add new formulas, change formulas, delete them, rearrange them.

• Final

  The check box "Final" declares a formula as a post transform formula: This means, applying the formula does not have any influence on the next iteration, but only is applied to the current iteration in order to "transform" the current pixel. See also Theory

• Hide

  The check box "Hide" lets you hide the current formula, i.e. disables it. It's effectively the same as deleting a formula.