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About Fractals
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| A fractal is generally "a rough or fragmented geometric shape that can be split
into parts, each of which is (at least approximately) a reduced-size copy of
the whole," a property called self-similarity. The term was coined by Benoît
Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or
"fractured." Because they appear similar at all levels of magnification,
fractals are often considered to be infinitely complex. Natural objects that
approximate fractals to a degree include clouds, mountain ranges, lightning
bolts, coastlines, and snow flakes.
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| The Mandelbrot set is a famous example of a fractal. |
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A closer view of the Mandelbrot set. |
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| More information on
fractals
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| The Mandelbrot set
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| The Mandelbrot set, discovered in 1980 by Benoît Mandelbrot, is probably the
most famous fractal. Like Julia sets, it is generated by a very simple formula,
but it is incredibly complex. The Mandelbrot set is loosely self-similar: parts
of the original fractal appear again when zooming in, but often deformed and
with different ornaments. This is what makes it so rewarding to zoom into this
fractal: you never know what you will see next.
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| More
information on the Mandelbrot set
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| Julia sets
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| One of the most basic fractal types is the family of Julia sets, discovered by
the French mathematician Gaston Julia during the first World War. Julia sets
are created by a simple formula with one complex parameter called C or seed.
This parameter can be varied to create many variations. Julia sets are also
self-similar.
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| More information
on Julia Sets
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![Julia Set for C = [-0.4, 0.6]](images\image3.png) |
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| Julia Set for C = [-0.4, 0.6]. |
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| Where to start
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| Now that you know a bit more about fractals, you are probably wondering how to
produce these with Utimate Fractal. By default, Utimate Fractal opens with a
standard Mandelbrot fractal, so the easiest way is to take this fractal and
start zooming. Click and drag inside the fractal window to zoom in. Click the
right mouse button to zoom out. Ultimate Fractal has many more possibilities,
but it is a good idea to start with simple zooming to get a feeling for what
fractals are and how Utimate Fractal works.
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| Click and drag inside the fractal window to zoom in. |
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The magnified portion of the fractal. |
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| Fractal Parameters
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| The Fractal Parameters Window shows the display center, the maximum number of
iterations, the magnification or scale and the complex parameter C used in the
Julia Set. You can change these parameters and press F5 (Refresh) or click the
Refresh button.
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| X |
The X value of the display center. Values can range from -2 to 2. |
| Y |
The Y value of the display center. Values can range from -2 to 2. |
| Iterations |
The maximum number of iterations in the calculation of the fractal. Values can
range from 1 to 10000. If the maximum iteration count is too small, the pixel
will be incorrectly colored (black). On the other hand, if the iteration count
is too large, many iterations will be performed and the fractal will be
calculated slowly. |
| Scale |
The magnification. A magnification of 200 times displays the
entire fractal. |
| X (C) |
The X value of complex parameter C used in the Julia Set. |
| Y (C) |
The Y value of the complex parameter C used in the Julia Set. |
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| The Fractal Parameters Window shows the display center, the
maximum number of iterations, the magnification or scale and the complex
parameter C used in the Julia Set. |
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| Zooming in and out
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| Click and hold your left mouse button and drag inside the fractal window to
zoom in. Click the right mouse button to zoom out. To reposition the fractal,
click the left mouse button to select a point in the fractal. This point will
become the new center in the fractal window.
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Zoom In (F9, Left Mouse Drag). |
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Zoom Out (F10, Right Mouse Button). |
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| Colors
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A color style defines how fractals are colored. The fractal formula creates the
basic shape of the fractal, and the color style provide a way to color that
shape. This gives you the flexibility to freely combine color styles with any
fractal. Ultimate Fractal makes it easy to change between color styles. Simply
select your style from the Options menu. There are 4 Colors to choose from:
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| Gradient |
The pixels in the fractal are colored according to the caculated index value in
a linear gradient. |
| Gradient 3D |
3D effect added to the Gradient style. |
| Hue Variation |
The Hue component of the pixel is changed according to the caculated index
value. |
| Hue Variation 3D |
3D effect added to the Hue Variation style. |
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The Randomize Colors command (F6) allows you to generate random
colors. |
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The Edit Gradient command allows you to edit and
change the gradient. |
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The Open Gradient command opens a gradient (not the
other parameters) of a previously saved parameter file (*.fractal). |
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| The Gradient dialog allows you to modify the gradient. Change the colors by
clicking one of the colors. Drag the position sliders to change the positions
of the interpolation colors. The color positions in the control specify
percentages of distance along the gradient line. For example, a value of 20
specifies that this point is 20 percent of the total distance from the starting
point. The positions in this control are represented by values between 0 and
100, and the first color in the gradient must be at position 0 and the last
must be at position 100. Check Alternating Colors to use two alternating
colors.
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| The Gradient dialog allows you to modify the gradient. Change
the colors by clicking one of the colors. Drag the position sliders to change
the positions of the interpolation colors. Check Alternating Colors to use two
alternating colors. |
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| When Ultimate Fractal calculates a fractal, it does not immediately calculate a
color for each pixel. Instead, it calculates an intermediate index value
. A gradient translates index values to colors. Since only the index values are
stored, the colors and color style can be changed without having to recalculate
the fractal. Here is an example of the same fractal for three different
gradients.
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| Undo and Redo
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| You can undo and redo your actions by clicking on the Undo and Redo buttons or
by clicking on the History list next to the fractal window. Use the Reset
button to restore the default Mandelbrot and Julia parameters.
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Undo (Ctrl + Z). Undo your last action. |
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Redo (Ctrl + Y). Redo your previous action. |
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Reset (Ctrl + R). Restore the default Mandelbrot and Julia
parameters. |
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| Favorites
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The Favorites list gives you a convenient way to organize and access frequently
used fractal parameters. Like bookmarks in a web browser, the Favorites list
helps you quickly access frequently-used items. With your fractals on the
Favorites list, you can open them without browsing the file system. When you
open an item only the fractal parameters are loaded, not the color information.
Use the File Open command to open the fractal parameters including color
information. The Favorites folder is located in the application directory
(C:\Program Files\Pop Art Studio\Fractals).
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The Add to Favorites command (Ctrl + F) adds the
fractal parameters (not the color style or gradient colors) to your Favorites
list. |
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The Organize Favorites command allows you to delete fractals from
your Favorites list. |
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| Opening and saving
fractals
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| Fractals parameters are saved to fractal files (*.fractal). A fractal file
contains a single fractal and all the information required to restore it. The
calculated pixels are not saved. Use the Save Image command to save the fractal
in image format (BMP, JPG, GIF, PNG, TIF). Choose the image size or a
predefined image size and the image resolution (default 180 dpi). You can use
the Open command to open a previously saved parameter file (*.fractal). The
Recent Files list displays a list of parameter files that you most recently
used.
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The Open command (Ctrl + O) opens a previously saved
parameter file (*.fractal). |
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The Save Parameters command (Ctrl + S) saves the fractal
parameters. |
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The Save Image command saves the fractal in image format (BMP,
JPG, GIF, PNG, TIF). |
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The Print command (Ctrl + P) allows you to print the fractal in
image format. |
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| The Image Size dialog. Choose the image size or a predefined
image size and the image resolution. |
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For comments, questions and suggestions, please send email to:
contact@fotoview.nl.
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