Dragon Flame

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Dragon Flame Examples

Fractal: Dragon Flame

Dragon Flame 01
Dragon Flame 01

Fractal: Dragon Flame

Dragon Flame 02
Dragon Flame 02

Fractal: Dragon Flame

Dragon Flame 03
Dragon Flame 03

Fractal: Dragon Flame

Dragon Flame 04
Dragon Flame 04

Fractal: Dragon Flame

Dragon Flame 05
Dragon Flame 05

 

The Dragon Flame examples each define a Dragon fractal altered by a Flame Transformation.

Several Dragon fractals are described on the Levy Dragon and Heighway's Dragon pages on Larry Riddle's Classic Iterated Function Systems site. A Flame transformation is applied to the Dragon fractal attractors to vary the design.

Change the Dragon Properties

Select the equation's properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Dragons
            Properties

Change the Dragon property to try out the predefined dragons, or set the Angle 1 and Angle 2 properties directly.

Change the Flame Transformation Properties

Select 1 of the transformation's properties pages:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Dragons
            Transformation Array
                Flame Transformation
                    Base Affine Transform
                    Post Affine Transform
                    Flame Variations
                    Flame Variation Arguments

Change the properties found on these pages to define the Flame transformation..

The Flame transformation's properties are found on 4 pages. Base Affine Transform and Post Affine Transform define affine transformations, and Flame Variations and Flame Variation Arguments define a set of non-linear transformations called flame variations.

The affine transformations Base Affine Transform and Post Affine Transform, are applied before and after the set of non-linear flame variations, respectively. Each affine transformation is composed of a series of simple transformations, applied one after the other, as defined on the respective properties page.

The remaining 2 pages define the flame variations. A flame variation is a non-linear transformation (i.e., complex function). The Flame Variations page determines the weight assigned to each variation. Any variation with a weight of 0 is not applied. The Flame Variation Arguments page holds the arguments, if any, for the variations with non-0 weights. After you set the weights for the variations you want to use, select the Flame Variation Arguments page to set the corresponding arguments, if any.

Change the Transformation

You can apply a transformation to the fractal.

Execute the Home command on the View menu of the Fractal Window to reset the fractal to the default position/magnification before you adjust the transformation. Then change the transformation and Zoom In to interesting areas of the transformed image.

To apply a transformation to the fractal, select the Identity transformation's page:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            Identity

Set the Based On property to one of the available transformations, select the transformation's properties page (found under the transformation in the page hierarchy), and play with the properties found there.

 

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