This short tutorial will introduce you to the most important functions of EasyFractal. Of course, such a brief intro shows only a short selection of the numerous possibilities offered by EasyFractal. The remaining chapters provide a more detailed description of all available functions.
We hope you enjoy working and playing with EasyFractal and experience lots of fun during your discovery journey into the depths of the fractal universe!
The 10 minute tutorial consists of seven learning steps:
First load the picture â•¥Mandelbrotâ•™ from the folder Fractals:2D-Fractals. This is the well-known Mandelbrot's Fractal; a symmetrical figure seemingly placed on its side.
1 - Now please click on a spot in the green border area of this black figure. The best spot is the clearly visible notch at the bottom side of this figure. Keep the ALT key depressed during this operation and zoom into the fractal.
2 - Repeat the procedure several times. Make sure not to zoom into black areas. The spot you click on with your mouse will become the center of the picture next time you zoom.
3 - Try to hit a nice rosette. You will notice that the deeper you zoom into the picture the more interesting the structures will become, but the calculation will also take longer.
4 - If you have found an interesting rosette, you will notice that it contains a large black area right in the center. Our task is now to fill this hole with content. To this purpose, open the Fractal Editor and place the cursor into the input field of the Iterations option. Now replace 256 with 1024. Confirm with Execute. A short calculation time later, and new structures appear in your picture where the black hole used to be. If you wish, you can now zoom into these new structures as described under 1.
5 - Now stop. Use the mouse to click on the center of the picture while keeping the CTRL key depressed simultaneously. Keep both keys depressed and watch the reverse zoom. Let go of the keys before the Mandelbrot's Fractal disappears into the endless depths of the fractal universe.... However, if this should still accidentally have happened, simply reload the picture.
6 - Now use the mouse button to draw a frame around one of the small black thickened areas of the antenna of Mandelbrot's Fractal. Then select the Calculate Block in Same Window menu item from the Fractal menu. The marked area will now be enlarged so that it fits into the existing window exactly. Repeat this process to examine areas of interest to you. A marked block can also be changed subsequently by keeping the SHIFT key depressed.
1 - From the File menu, select Open ... and load the picture called "Mandala" located in the "Fractals:2D-Fractals" folder. We would like to take this opportunity to point out once more that all of the files located in the "Fractals" folder are not real pictures but only the information about the fractal required by EasyFractal to load the file and to calculate and display the corresponding picture.
2 - Once the picture has been calculated, click on one of the arrows at the side or bottom scroll bar and view the surrounding area of the fractal rosette. All new image sections are recalculated in realtime when scrolling within an EasyFractal image. In theory, you can scroll endlessly to the left or the right, top or bottom; however the size of the virtual screen imposes certain limits. To scroll beyond these limits and explore the entire fractal universe, all you have to do is redefine the center of the virtual window (e.g. by a zoom step).
Tip: Reverse zoom from the "Mandala" fractal (mouse click + CTRL key). After about 70 zooming steps you can see the origin of the "Mandala" image within Mandelbrot's Fractal. More information about the zoom increments, etc. is listed in the chapter The Fractal Editor.
1 - Return to the original position of the rosette Mandala (or load the picture again if you are having trouble hitting the exact center). Open the Palette Editor you can then use to change the colors of your fractals in many different ways.
2 - Enter a 0 into the Start Color field of the Palette Editor and 255 into the Target Color field. Click on the Effects tab. Now go to Rotation and click on one of the two arrows at the right, next to the associated input field. Keep the mouse depressed. Rotating the color palette has a fabulously colored kaleidoscope effect in the opened picture window.
3 - Load a new color palette. To open a new color palette select Load ... from the Palette menu and then double-clock on the file "Ease.CTAB" located in the "ColorTables:Colors-256" folder. The new color palette has an immediate effect on the topmost image, resulting in a completely different picture. Details of the new color composition are displayed in the color ribbon of the Palette Editor. Go back to Rotation, cycle the new colors a bit forward and backward, and observe the continuously changing impressions and structures caused by the changing colors.
1 - You have already calculated one Mandelbrot set, the classical Mandelbrot's Fractal to be exact, which is loaded automatically when starting the program. To try out another formula, select New ... from the File menu.
In the Fractal Editor, now enter a name for your new fractal and then click on the Function tab. A popup menu appears where you can select from different iteration functions. Z^2 is the default setting and results in the well-known Mandelbrot's Fractal. Now select the third function X^2-Y^2,X*Y*2+Y and click on DefaultAll located at the lower edge of the window. This sets all parameters of the Fractal Editor to default values. Click on the FS tab and deactivate the Finestructure. All that is left to do is to click on Execute and a new window opens displaying the desired fractal.
2 - A somewhat misshapen shape appears with completely different structures inside of the border areas than the baroque ornaments you know from the Mandelbrot's Fractal.
A Julia set is defined for each point of a Mandelbrot set. The selected point is always incorporated into the calculation in the form of a parameter and thus determines the appearance of the Julia set.
3 - Now have the program calculate a Julia set for a point of this Mandelbrot set. Use the option Generate Julia Set from the Fractal menu. Once you click on this menu option, the cursor will change into a cross as soon as a window with a Mandelbrot set is the topmost window and you move the mouse across the picture. Now select a point within the image. It is best to begin with the border area, where the colors appear to be more even (left side).
4 - If clicking with the mouse, the selected parameters are imported to the Fractal Editor. Just confirm with Execute. The new window now displays a Julia set for the previously selected point of the Mandelbrot set. Again, you can zoom into and out off the picture, change color palettes, and cycle colors. Experiment with different points of the Mandelbrot set and observe how the associated Julia sets change as well.
Tip: To find aesthetically pleasing points within this Mandelbrot set, pay attention to less turbulent, smoother areas when zooming.
(If you do not find any such areas, load the fractal named "Wave" located in the "Fractals:2D-Fractals" folder, which has such a nice spot. Zoom into the eye of the spiral and use the program to try and calculate the black hole in the center more deeply, as described in A-4 (Iterations).
1 - Open the picture named "Galaxy" located in the "Fractals:2D-Fractals" folder.
2 - Go to the Palette Editor and activate Start Color. Use the mouse to click on an especially bright color within the color ribbon of the Palette Editor. The selected color number (also: color index) and the associated color hue are now displayed at the top.
3 - Activate End Color and select another color from the color ribbon. This time, choose a dark color that is about 4 cm (approx. 1.5 inch) removed from the first selected color.
4 - Click on Color Gradient.
5 - Now set the Start Color manually to 0 and the End Color to 255. Go to Rotation and keep the mouse key depressed on one of the two arrow keys to check the new coloration.
6 - Click again on Start Color to select another color from the color ribbon. Now click on the Pick Color button and use the eyedropper to select a color from anywhere on the entire desktop. After clicking with the mouse, this color is now listed in the color ribbon as a thin vertical line.
7 - Repeat the same process with the End Color, only now do not use Pick Color but use Change Color instead. The Mac OS Color Picker opens and you can use this tool to select any desired color.
8 - Click on Color Gradient and check the result as described in 5 .
9 - Repeat these steps until you like the coloration. Then save your new color palette with Save As ... from the Palette menu. This palette can be used for other fractals as well.
Tip: To receive a smooth and gradual color gradient, set your computer to "millions of colors".
1 - Click in the window with the classical Mandelbrot's Fractal. If this fractal is no longer visible on screen, simply reload it.
2 - Now zoom the small thickened area of the antenna until it has reached the size of the original Mandelbrot's Fractal. Additional small thickened areas appear on the antenna. Repeat the process approx. 5 times.
Now click on the 3D tab located in the Fractal Editor. A button is displayed at the top left labelled 3D Display. Click on this button. EasyFractal now interprets the information contained within the picture three-dimensionally. What you now see should resemble a landscape with a mountain in the center.
3 - Of course, the colors are rather unsuited for this landscape image. You can try (as described in the previous chapter) to modify the palette yourself until you find some suitable colors or just use a different predefined palette. For example, three-dimensional images do well with the palettes "DeepImpact" and "Volcano" located in the "ColorTables:Colors-256" folder.
4 - Now select the category General and set the number of iterations to 300. If the number of iterations is higher than the number of colors in the palette, you can use this trick to turn the mountain into a crater since EasyFractal assigns the colors and/or height values in an oscillating manner. Of course, you still have to click on Execute.
5 - Now return to the 3D area of the Fractal Editor and experiment with the slider bars. Use the sliders to change the view angle, the peak, and other parameters.
6 - Now click on Rotation. Since the center of the picture is probably now outside of the window (due to the many zoom steps), you should first redefine the center of the picture by clicking on the New Rotation Center button. Then use the slider bar to rotate the picture.
Note: The picture has to be newly calculated every time it is rotated. This might take too long for a realtime depiction, depending on the speed of your computer and the selected screen section. In these types of cases, we recommend to rotate the picture in smaller steps by clicking next to the slider button or by manually setting the desired angle and then pressing the RETURN or ENTER key or clicking on Execute.
1 - Click in the window with Mandelbrot's Fractal. Just reload if necessary.
2 - Now click on the FS tab and then on the Fine Structure button. The red area now has a very 3-D look about it. Other parameters and a different palette have to be set in order to try out the other functions of this dialog window. Just click on Default Palette in the Palette Editor, then on Default All in the Fractal Editor, and then on Execute..
Additional spheres appear and the normally black area of the Mandelbrot's Fractal now has structure.
3 - Now, use the sliders of the FS dialog in succession. Click on Execute after every change. The color progression becomes finer with a larger Parition while the oscillation creates additional waves in the different areas of the fractal.
4 - Now, click on the Parameter tab. A popup menu for different escape conditions is located at the upper right. Select a different escape condition (e.g. Hyperbola). Again, click on Execute. The resulting fractal has the same elements but these elements are depicted entirely differently.
5 - Now it is your turn to try out different values with the lower three parameters. Start by changing the numbers slowly to easily observe the type of changes taking place.
Tip: We recommend activating the New Fractal checkbox, which will make it easier to compare modified parameters and their respective effects. The new image is then depicted in a new window and you can compare it easily with the previous one.
