Fractals and FracHunt

FracHunt is a program that lets you explore the most famous fractals,

FracHunt can be divided in the main control window and the render window.

The control window contains all the information to render a certain fractal .

The render window contains the rendered fractal.

The control window

This chapter will explain all the controls in the control window.

The control window is divided into three areas:

Render Area: Specify the viewport of the fractal to be rendered
Algorithm's: Tell FracHunt which Fractal you would like to render and how to color it.
Options: Miscellaneous options like window size etc.

The next chapters will explain the controls in those areas

The render area lets you specify which part of the fractal you would like to render. Most fractals only show interesting parts in certain areas. For instance a Mandelbrot fractal only has interesting parts within the [-2,-2] to [2, 2] range.

Fractals are rendered in the complex plane. This means the X-Axe is the Real Axe while the Y Axe is the imaginary Axe. See your math book for an explanation on complex numbers. You can find a very basic introduction in a following chapter. However you do not have to understand complex numbers to use FracHunt.

Of course X-Start shouldn't equal X-End and Y-Start shouldn't equal Y-End. If Y-End is smaller than Y-Start then the fractal will be rendered reverse. The same applies when X-End < Y-End. If your math has become a little rusty, -10 is less than 1.

Algorithm's

The most important part in the algorithm's section is the 'Set' Drop Down list. This parameter let you select which fractal to render. Later on an explanation is given of all fractal types.

Some fractal types let you specify a constant. Depending on the type of fractal this constant has a certain meaning. For a Julia type fractal it is for instance the C in Z(k-1) = Z^2 + C. If the C(Re,Im) controls are disabled then there is no Constant to set for the particular fractal.

Fractals are colored by a certain strategy. The simplest strategy is just to take the number of iterations to reach a certain number and then assign a color to the number of iterations. Assigning a color to a number can be done in an infinitely number of ways. The coloring algorithms just supplies a number of ways to color a fractal. Some Color algorithms have the possibility to give an indication of the number of colors you would like to use. Don't take this to be the absolute number of colors in the final fractal but more as an indication. The higher the number of colors the longer it will take to render but the more refined the resulting picture will be. In one of the next chapters a more in depth explanation of all coloring algorithm's is given.

Options

With the option's section section you have control over other aspects of the program not directly related to the fractal itself.

The Width and Height are the dimensions of the window that will pop-up when the render button is pressed. If the 'Aspect Ratio' is checked the window's area will be Width * Height and the Width/Height Ratio will equal ( XEnd - XStart ) / ( YEnd - YStart ). This will preserve the aspect of the fractal. And of course it will result in a window which will not be exactly sized 'Width' by 'Height'

The samples drop down box makes it possible to start one of the predefined Fractals. Just selecting one of the Samples and pressing 'Render' get's you going. It is also a great starting point for your own fractal. Select one of the samples then adjust a few parameters and press render.

The Show values check box will render a box with fractal type and start and end coordinates in the render window. However this will only appear when the render window is large enough to show those values.

Aspect ratio, when checked, will preserve the Height/Width ratio of the original fractal. You typically DON't want have it set when rendering for a windows background,since it will adjust your entered height and width.

When the 'On Top' is checked the control window will stay on top of all other windows. Other windows that also have 'On Top' set like the help window however may appear above the control window.

The Desktop check box will make FracHunt serialize its state to persistent storage ahum.., I mean will save FracHunt's desktop to disk. When you start FracHunt again, all rendering windows and the state of the control window will reload from disk. Windows that were rendering when exiting FracHunt will continue rendering when FracHunt is started again. Checking this box however might require a lot of disk space if you have a lot of large render windows open.

The render window

This window will show you the, possibly partially, rendered fractal. However this window also has a few options and features that I will discuss.

Selecting a new render area

You might have noticed that it is quite cumbersome to enter new values in the control window. Luckily you can avoid this because the render window will set them for you by selecting a certain area.

The idea is to zoom in on an already rendered fractal. This can be done as follows:

First render a fractal, for instance by using one of the predefined values in the sample box.
Then left click you mouse in the render window and drag.
Make the rectangle large enough to enclose the area on which to zoom in.
Release the mouse button.

This will set the correct coordinates in the render window. It will also set the coloring algorithm and number of colors to the ones used to render that window previously.

The next thing to do is change number of colors, coloring algorithm, window size and options to what you want them to be.

Finally press render to get a new fractal window.

Using mandelbrot as an index in the Julia set

The way mandelbrot and julia fractals are related actually makes mandelbrot fractals an index in the julia set. A special options is available on the popup menu with the title "Set Constant". This option will set the constant in the control window. If you select the corresponding julia set after that and render that fractal you get a julia set fractal which resembles the rendered mandelbrot fractal. Of course if the point itself is contained in the set at that point the mandelbrot and julia set are exactly the same.

The following mandelbrot sets are an index in the corresponding julia set:

Mandelbrot set Related julia set
Mandelbrot Julia set
Mandelbrot^3 Julia set^3

Mandelbrot set	Related julia set
Mandelbrot	Julia set
Mandelbrot^3	Julia set^3

To use this feature do the following

Render a mandelbrot type fractal.
Press the right mouse button and select 'Set Constant'
Select a part from the render window by dragging your mouse with the left button pressed.
Change the algorithm to the corresponding Julia set fractal.

Save your rendered fractal

Of course after that overnight render you might want to save your fractal. There are three ways to save your fractal as:

FracHunt's native format ".Fra"
A windows 24 bit windows bitmap
32 bit tga file useful for POV-Ray height fields.

The first has the advantage that you can load the fractal again with the options on the File->Load menu in the main control window. If the fractal didn't finish rendering it will continue.

The second option is the way to go if you want to use your rendered fractal in some other way like for a windows background, POVray or in a graphics program.

The third should be used if you want to use your fractal as a POV-Ray height field. The chosen coloring algorithm should have been 'POV-Ray height field'.

See the Fractal's properties

By selecting "Properties" from the speed menu you can see the properties of the render window. On the properties box is an option "Set" this will set the values in the control window.