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TUTORIAL

This tutorial provides an overview of Explorador FF 7.7, hereafter EFF. With this information you will learn how to use the application, but for better results a basic idea of fractal geometry would be needed.

 

CONTENT

  1. Explore a fractal

  2. Change the type of fractal

  3. Modify parameters of a function

  4. Change the colouring method

  5. Apply and manage palettes

  6. Apply and manage orbit traps and patterns

  7. Rotate the fractal

  8. Setting options

  9. Working with points

  10. Export and import parameters

  11. View the Julia sets of a fractal

  12. Creating maps of Julia

  13. Creating cellular noise

  14. Creating stereographic projections

  15. Creating kaleidoscopic images

  16. Creating diffusion-limited aggregations

  17. Creating Sierpinski designs

  18. Creating Pythagoras tree

  19. Automate processes with tasks

  20. View information about the fractal

  21. Hibernation of processes

  22. Tips

 

EXPLORE A FRACTAL

Open a new canvas from "File" menu or press "Control + N". If you want to load a specific type of fractal, hold the pointer on "New canvas of type" and choose the type of fractal in the secondary menu displayed.

To explore a fractal you can do the following actions:

  • Zoom in

    With the left mouse button, click on any point over the image and, still holding, slide the mouse in order to create a selection area. Release the button so you zoom in the selected area.

    Zoom in operation

  • Zoom out

    With the right mouse button, click on a point over the image and, still holding, slide the mouse in order to create a selection area. Release the button so you zoom out the selected area.

    Zoom out operation

  • Centering

    There are three options:

    1. Double-click on a point of the image to centre it.

    2. Click on a point of the image while the "F" key is pressed.

    3. With the middle mouse button, click on a point over the image and, still holding, slide the mouse in order to create a selection area. Release the button so you centre the central point of the selected area on the canvas.

      Centering operation
  • Scrolling

    There are two options:

    1. Press and hold the "Shift" key while you click with the left mouse button on a point over the image in order to fix an origin point. Without releasing both buttons, slide the pointer to the destination point. Release the mouse button to confirm the scroll from the origin point to the destination point.

      Scrolling operation 1

    2. Press and hold the "Control" key while you click with the left mouse button on a point over the image to "catch it". Without releasing both buttons, slide the pointer to drag the image to a new position. Release the mouse button to confirm the image scroll to the new position.

      Scrolling operation 2
  • Rotation

    * Rotation is not available for the special fractals Bifurcation, Lyapunov and Buddhabrot.

    There are two options:

    1. Press and hold the "Shift" key while you click with the right mouse button on a point over the image in order to fix the rotation centre. Without releasing both buttons, slide the pointer horizontally to rotate the image. Release the mouse button to confirm the image rotation.

      Scrolled rotation

    2. Press and hold the "Control" key while you click with the left mouse button on any point over the image. Without releasing both buttons, slide the pointer horizontally to rotate the image around its central point. Release the mouse button to confirm the image rotation.

      Centred rotation

      This rotation type can be performed more accurately in the form "Edit" that will be seen later.
  • Resicing

    Resize the window so the canvas adapts itself to the window. While you are performing this operation, the canvas size is shown in the window frame.

    Resizing operation

    You can also resize a canvas with the size and aspect-ratio adjustment options, available in the "Window" menu.

  • Get a satellite view

    Click on "satellite view" in "Edit" menu or press "Control + Up" in order to zoom out and watch the full fractal. With this operation the central point of the origin image will remain centred on the canvas.

    Satellite view

  • Get a main view

    Click on "Main view" in "Edit" menu or press "Control + Space" in order to fit a full view of the fractal in the canvas. With this operation the reference of the central point of the origin image will be lost.

    Main view

All actions that require to perform a selection with your mouse, when they are finished, will set the centre point of the selected area on the canvas centre. These actions can be cancelled pressing "Escape" before releasing the left mouse button.

Learn more...
In order to show the images faster, it is recommendable to use a small canvas when you are exploring and, once you get the wished aspect, resize it to generate the final image.

To avoid unwanted image frame changes caused by resizing, you must keep in mind the aspect ratio wanted for the final image from the beginning. For example: if you want to generate an 1,600 x 1,000 px image it is recommendable to work with a small canvas with proportional dimensions. The aspect ratio you want is 1,600/1,000 = 1.6, thus any canvas with that aspect ratio will allow to avoid the problem, i.e. 320 x 200 px.

When you open a new canvas without specifying the type of fractal, it loads the last selected type.

 

CHANGE THE TYPE OF FRACTAL

Open the tool "Parameters" from the "View" menu or press "Control + Alt + P". This tool has one tab page per type of fractal (zone 1 in the image) with their parameters (zone 2 in the image) and an area of common parameters to all the fractals (zone 3 in the image). Select the different tab pages in order to change the type of fractal.

EFF 7.7 version includes these fractals: Mandelbrot, Phoenix, Burning Ship, Newton, Halley, Secant, Householder, Schröder, Steffensen, Laguerre, Nova, Mandelbox 2D, Bifurcation, Lyapunov and Buddhabrot. These fifteen main functions allow to create up to 56 different types of fractal.

Mandelbox 2D, Bifurcation, Lyapunov and Buddhabrot are special fractals and some functions that are described in this tutorial do not apply to these fractals.

Parameters form - Fractal types

If there are several canvases opened, this tool shows the parameters of the "Active canvas", which is the last canvas that has been activated. This also applies to other tools that will be seen later. The "Active canvas" is identified with an arrow-shaped icon.

Active canvas

Learn more...
Every canvas has an independent history of changes for each type of fractal, so that when switching to another type, it does not lose the history of changes of any of them. You can access this history of changes in "Edit" menu by clicking on "Undo" and "Redo", or press "Control + Z" and "Control + Y" respectively.

When exploring the fractal, a change of colour may happen in the icon of "Active canvas", from grey to orange. This means that you have exceeded the computer's processing capabilities.

Zoom limit

 

MODIFY PARAMETERS OF A FUNCTION

Every fractal is generated from an algorithm. This algorithm has certain parameters that can be modified. Open the tool "Parameters" from the "View" menu or press "Control + Alt + P" and change the values in order to create variations in the original fractal. Press "Enter" key in the parameter field to apply the changes.

Parameters form

The common parameters to all fractals are (zone 1 of the image):

  • Number of iterations (positive integer)

    Indicates how many times the function will be recalculated. A high value gives the fractal more "depth" to do a zoom in, but it will slow the calculation. The iterations should be increased gradually only when necessary.

  • Exponent of Z (positive or negative decimal)

    * This parameter cannot be modified for the special fractals.
    It is the exponent of the variable "Z" and it allows to create mutations in the original fractal.

  • Central coordinates (complex number)

    This parameter allows to centre a determinate point of the fractal within the canvas by indicating its coordinates. When exploring the fractal, this value changes with the coordinates of the point of the fractal that corresponds with the centre of the canvas.

The specific parameters of the fractal type are:

  • Julia's constant (complex number)

    When you activate this parameter, the variable "C" is changed to be constant with the set value and the fractal is drawn through "Julia's method".

    When this is deactivated, the value is not used and the fractal recovers the previous status in the activation through "Mandelbrot's method". In this case, when exploring the fractal, the default value for the "C" constant changes corresponding to the coordinates of image's central point.

  • Distortion constant (complex number)

    This constant distorts the fractal aspect. If the value is zero, it has no effect on it.

  • Relaxation constant (complex number)

    This constant adjust the fractal complexity. If the value is one, it has no effect on it.

  • Initial value of Z (complex number)

    It is the value of the variable "Z" used to start iterating the function and it allows to create mutations in the original fractal.

  • Initial value of X (decimal number)

    It is the value of the variable "X" used to start iterating the function and it allows to create mutations in the original fractal.

  • Lyapunov's secuence (binary sequence)

    It is a sequence of values 0 and 1 that determines the value used to iterate the function.

  • Inverse

    This switch inverses the variable that runs the plane for calculation purposes and allows to create a variation of the fractal.

Learn more...
Complex numbers have a real part and an imaginary part, and they are represented as "Z = (a + b i)", where "a" is a real number and "b" is an imaginary number, multiple of the imaginary unit "i". The numbers "a" and "b" can be positive or negative decimals and the imaginary unit "i" is a constant that equals to square root of -1.

To optimize the calculation process it is recommendable to increase the number of iterations only when necessary. For example, you may increase it gradually when you zoom in, or decrease it when zooming out.

 

CHANGE THE COLOURING METHOD

* The special fractals use specific colouring methods that cannot be changed.

In order to draw a fractal it is necessary to define a colouring method. EFF uses the "Escape time" algorithm by default. To use another method, click on "Settings" menu and hold the pointer on "Colouring method by default". Click on the method you wish to use by default in the displayed submenu.

EFF has the following colouring methods:

  • Escape time

    It colours the image according to the number of iterations reached during the calculation process.

    Escape time
  • Escape angle

    It colours the image according to the angle between the variable used to iterate and the horizontal axis during the calculation process.

    Escape time
  • Distance to a point

    It colours the image according to the closest distance to a point reached during the calculation process.

    Distance to a point

You can change the colouring method for a specific canvas in the "Colouring" tag in the form "Edit", which opens from the "View" menu, or press "Ctrl + Alt + E", where you will be able to use some advanced settings.

Edit form - Colouring

 

APPLY AND MANAGE PALETTES

* Each fractal type has its own predetermined palette associated, except for the special fractals Bifurcation, Lyapunov, Buddhabrot and Mandelbox 2D in its X-Ray version. To change the colour of the two former fractals use "Colour in" (zone1 in the image) and for the third one, use the option "Colour the last iteration in..." from the "Options" form (it will be seen later).

To use a different palette, click on "Edit" menu and hold the pointer on "Apply palette". Click on the palette you wish to apply in the displayed submenu. This option is also available in the "Palettes" tag in the form "Edit", which opens from the "View" menu, or press "Ctrl + Alt + E", where you will be able to use some advanced settings:

  • Check the "Current palette" box to get a preview of the "Active canvas" palette or to view its number of colours.

  • To scroll the colours of the palette, you can click with the left mouse button on preview and slide the pointer. You can see the scrolling value below the preview. Then click on "Apply".

Edit form - Palettes

To manage palettes you have the following functions:

  • Import palettes

    Predetermined palettes are built in the application, but there is a possibility to add new palettes. To do this, click on "Import palettes" in "File" menu. In the dialog box that opens, select one or more palette files with extension F2C or F2ZC, and click on "Open".

    The new palettes are copied in the palettes folder of the application.

  • Delete a palette

    Click on "File" menu and hold the pointer on "Delete palette". Click on the palette you want to delete in the displayed submenu.

    The built-in palettes are shown up with an asterisk and they cannot be deleted. These are:

    1. Random B&W: its grey hues change randomly every time it is applied.

    2. Random RGB: its colours change randomly every time it is applied.

    3. Random R: its red hues change randomly every time it is applied.

    4. Random G: its green hues change randomly every time it is applied.

    5. Random B: its blue hues change randomly every time it is applied.

    6. Rainbow: decomposition of white colour in the rainbow colours.

    7. Striped: predetermined palette in these fractal types: Newton, Halley, Secant, Householder, Schröder, Steffensen, Laguerre, random Julias and Mandelbox 2D.

    8. Continuous: predetermined palette in these fractal types: Mandelbrot, Phoenix, Burning Ship and Nova.

    9. B.Default: predetermined palette associated with the type of fractal, really is "Striped" or "Continuous".

The options of palettes management are also available in the form "File", which opens from "View" menu, or pressing "Ctrl + Alt + F".

File form - Palettes

Learn more...
Palette files can also been imported by dragging and dropping them in the EFF working area.

EFF palettes consist on a list of colours defined by its components "RGB". The components "R", "G" and "B" are values included between 0 and 255 separated by tabulation character. Every line represents a colour, and in most of palettes the first line uses to be black. The reason behind this is that when calculating a fractal with a number of iterations multiple of the number of colours of the palette, the points corresponding to the latest iteration of the function will always be drawn in black.

 

APPLY AND MANAGE ORBIT TRAPS AND PATTERNS

* Orbit traps are not available for the special fractals.

The "Orbit trap" is a special colouring method based on a pattern to be adapted to the fractal. EFF 7.7 version includes the following built in geometric patterns:

  • Horizontal, Vertical, Cross, Mini-Cross, Diagonal1, Diagonal2, X-Shaped, Mini-X-Shaped, Square, Hypercube, Circle and Torus.

EFF allows to apply the next types of orbit traps:

  • None: it is the default type and it is used to suppress the orbit trap. The fractal is drawn with the palette applied to the canvas.

  • Simple: it uses a built in geometric pattern to draw the fractal.

  • Multiple: it uses several built in geometric patterns simultaneously to draw the fractal.

  • Pattern: this trap uses an image file as a pattern and it is the only one that is not based on palettes.

To use a simple orbit trap, click on "Edit" menu and hold the pointer on "Apply orbit trap". Click in the pattern you wish to apply in the displayed submenu. This option is also available in the "Orbit trap" tag in the form "Edit", which opens from the "View" menu, or press "Ctrl + Alt + E", where you would also be able to choose other types of orbit trap and to modify the pattern features (zone 1 in the image):

  • To get a preview of the "Active canvas" orbit trap, you can check the "Current trap" box.

  • To scroll the orbit trap, you can click with the left mouse button on the preview and slide the pointer. You can see the scrolling value below the preview. Then click on "Apply" ("Add" or "Replace" if the orbit trap is "Multiple").

  • To change the rest of orbit trap properties, you can change their values with the adjusting controls and then click on "Apply" ("Add" or "Replace" if the orbit trap is "Multiple").

An EFF feature worth talking about is that EFF allows you to configure the adjusting controls in order to make a more accurate adjust of the parameter. You can do this by using an extra control that allows you to select the specific decimal position that you wish to modify (zone 2 of the image).

Edit form - Orbit traps

If the selected orbit trap is "Multiple", the patterns will be added or replaced in the "Multiple trap" designer, where they can be organized and applied as a whole.

Multiple trap form

There are differences between the "Simple" orbit trap (1) and the "Multiple" orbit trap formed by only one pattern (2) if the opacity is not the maximum. The first melts the overlapping and the second lets it be seen. Additionally, there is the possibility of splitting the palette's colours for the multiple orbit trap (3).

Orbit traps

To manage patterns you have the following functions:

  • Import patterns

    There is a predetermined pattern built in the application, but there is a possibility to add new patterns. To do this, click on "Import patterns" in "File" menu. In the dialog box that opens, select one or more image files with extension BMP, JPG or PNG, and click on "Open".

    The new patterns are copied in the patterns folder of the application.

  • Delette patterns

    Click on "File" menu and hold the pointer on "Delete pattern". Click on the pattern you want to delete in the displayed submenu.

    The built-in patterns are shown up with an asterisk and they cannot be deleted.

The options of patterns management are also available in the form "File", which opens from "View" menu, or pressing "Ctrl + Alt + F".

File form - Patterns

Learn more...
To create customized orbit traps you can draw a PNG image with transparent areas and import it as a pattern. When using this pattern, the fractal will be drawn with its image, and the transparent areas will let see what is underneath.

The drawing process adapts the pattern to the fractal's shape folding and stretching it, what can make the result to be distorted if the pattern has low quality. In order to avoid this you should use patterns with big dimensions, that will allow you to zooming in even deeper without losing the quality all too soon.

Pattern files can also been imported by dragging and dropping them in the EFF working area.

 

ROTATE A FRACTAL

* Rotation is not available for the special fractals Bifurcation, Lyapunov and Buddhabrot.

To adjust the fractal rotation, click on "Edit" menu and hold the pointer on "Rotate". Click the rotation that you wish to apply in the displayed submenu.

Rotation result

This option is also available in the "Orbit trap" tag in the form "Edit", which opens from the "View" menu or press "Ctrl + Alt + E":

  • To see the "Active canvas" rotation you can check the "Current rotation" box.

  • To adjust the angle, you can click with the left mouse button on preview and slide the pointer. You can see the scrolling value below the preview. Then click on "Apply".

  • For a more accurate adjusting of the angle you can use the adjusting control and then click on "Apply".

Edit form - Rotate

 

SETTING OPTIONS

Open the form "Options" from the "View" menu or press "Control + Alt + O". This form has an area of options that can only be changed when the "Active canvas" is not in calculating process (zone 1 on the image) and another with options that can be changed at any time (zone 2 on the image).

Options form

The available options out of the calculation process are:

  • Activate anti-aliasing filter with grille...

    * Anti-aliasing filtering is not available for the special fractals Bifurcation and Buddhabrot.

    "Anti-aliasing" is a method that allows obtaining higher quality images, closest to the fractal, using additional colouring operations. This drawing method increases the process time, so it is recommended to keep it disabled and use it just for final images that are going to be saved afterwards. To active it, check the corresponding box or select the grille size in the combo box.

    You can apply the "Anti-aliasing filter" punctually to an image without enabling the option. To do this, open the form "Anti-aliasing filter" from the "View" menu or press "Control + Alt + A". Select the grille size and click on "Apply".

  • Colour the last iteration in... / Colour in...

    This option uses a determined colour to draw during the calculation of the last iteration. To active it, check the corresponding box or select a colour in the selection area.

    This colour is to be employed in the special fractals Bifurcation, Lyapunov and Buddhabrot.

  • Draw the last iteration over the orbit trap

    This option draws the area that corresponds to the last iteration of its formula over the orbit trap.

The available options at all times are:

  • Activate image refreshing

    This option refreshes progressively the image while it is calculating. It's recommended to have it disabled because it slows the calculation process.

  • Save image changes automatically

    This option saves automatically the image of the fractal every time it changes. The images are saved in "PNG" format in the images folder of the application, inside a canvas subfolder on which the option is enabled. You can open the images folder of the active canvas in "File" menu by clicking on "Open images folder of the canvas" or press "Control + Shift + O" (this folder is created when the first image is saved).

  • Activate fast scrolling

    * Fast scrolling is not available for the special fractals.

    When scrolling the fractal with the mouse, the previous image is used in order to not calculate the new image fully. Before saving the image after a fast scrolling it is recommended to recalculate it by pressing F5 or applying an "anti-aliasing filter". The canvas with this option activated is identified with an arrow-shaped icon preceded by two white lines.

Learn more...
The images that hold a high amount of different colours in small areas improve their quality if you apply the "anti-aliasing filter" with a big grille size. However, for images with big areas of the same colour, applying a small grille size would be enough. It is recommended to experiment with this in order to learn how to choose the optimal grille depending on the type of image, because in some cases a big grille size slows the calculation process and it provides a little addition to what a lower grid would.

The option "save image changes automatically" can be used combined with a task in order to get images, like movie frames, for building a video or animation (spanish) using an external application.

The option "Activate fast scrolling" can be activated by default for all canvas from the "Settings" menu. Before saving the image after a fast scrolling it is recommended to recalculate it by pressing F5 or applying an anti-aliasing filter.

 

WORKING WITH POINTS

An important feature of EFF is that it allows taking a snapshot of all the parameters and configurations needed to draw a fractal at any time. This information, denominated "Point", is registered in a file inside the application that allows recovering the image anytime.

During its running, EFF keeps in memory a list of the thirty last points, corresponding to closed canvases. This characteristic allows recovering a previously discarded point if this has not been overwritten already.

To administrate the points you have these functions:

  • Register a point

    Click on "Register point" in "File" menu or press "Control + R". In the form that opens write a name for the point, write a comment (optional) and -if you wish to- check the "Publish" box (view explanation bellow). Then click on "Register".

  • Publish a point

    Check the "Publish" box before registering a point. By publishing the parameters of an image you are collaborating to create an online library in an anonymous way, so you and other EFF users would be able to enjoy the best fractals afterwards.

  • Load a point

    Click on "File" menu and hold the pointer on "Load point". In submenu displayed, click on the point you want to load.

  • Rename a point

    Click on "File" menu and hold the pointer on "Rename point". Click on the point you want to rename in the displayed submenu. Write a new name and click on "Rename" in the form that opens.

  • Delete a point

    Click on "File" menu and hold the pointer on "Delete point". Click on the point you want to delete in the displayed submenu.

  • Recover a point

    Click on "File" menu and hold the pointer on "Recover point". In submenu displayed, click on the point you want to recover.

In the displayed submenus with the name of the registered points, if you hold the pointer over a concrete point, a label is displayed with the comment that was written when registered.

All described options can also be found in the form "File" that opens from the "View" menu or pressing "Control + Alt + F".

File form - Current point   File form - Registered points
File form - Recover point

Learn more...
Working with points is the most recommended option, because it avoids to remember all settings required to generate an image and thus can be easily retrieved for further work with it in a future.

If you create a shortcut to EFF executable and you add a parameter with the name of a registered point, when using it to run the application, it opens and loads the point indicated by the parameter.

 

EXPORT AND IMPORT PARAMETERS

EFF allows sharing points of the fractal through a function which exports all its parameters and configurations. This info can be employed by any EFF user in order to get the same point.

  • Export parameters

    Click on "Export parameters" in "File" menu or press "Control + E". Check that the image which parameters you want to export shows up in the form that opens, and select one of the following options:

    1. Include palette and pattern: if the image uses a palette or a pattern not built in EFF, it is recommended to apply this option. A dialog box will be opened when pressing the button in order to select the path to export the file of parameters.

    2. Only parameters: this option is designed to export the parameters of the images that use a built-in palette and pattern. The parameters will be exported to Windows' clipboard when pressing the button.

      Export parameters form

    The exported parameters can be attached to an email and be sent to another EFF user. For instance, the parameters of the image above are the following:

    oetythKl5tVnKtRe+CQ7tmFgnv4IitecPfR9Qu8To
    Ax9B6NOquYWmCkZAoI3QvS3GxisSOFPhWC2s
    Pl5WKZRBlh6U9C1U8qTqQ1N9fT/g9ACCOeCg8
    CwUfRXuiK86xQF6AhLSJpyQI/ojkQVtyMHTXek
    Mm1D0bo6giUe46zBGtXBhlHfMvER9ZxH8FRi7d
    pL5SKozN8DGe6BBg4qxwM+j3UTZRaIa2b0Luu
    MlxZ+BgkuS0nicIn3BWigea4flTDdlH76MKmQU5
    9b7vjyGm+DqQDYcvW7JrkW8XEmV8fe3R3DaK
    BA9E9M0c8ABN+D3jts2tOp487EGblLMUCdWxC
    0HnSxy8h3BQLkfJJwhIbtbCkE6kKoVRukVbP1Tqt
    AbgpkC1OIEoOcySyDh/avcjNYRIwZ7cwgpZqjPXg
    b2ylV0osUlU/kwhJq+u4pgfwON+0jCKqmUHB9Ji
    uNmJJFO3L9tXR2oPpds1T+6TchMDqNFiy96JJ5V
    GwShom8fwnAEhEqqVWEJvTNWU+ApOjqEQ0Y
    t9eh6MQbcJ3975OHV3cnMUDGzzMI82K6tMl4
    h5KHdj3lWBGSGACHmA0aSo216SLwPOGGg0fC
    sIFrvow933F+JTgXM48EkGHRhS+igYiAjaNFrqQa
    Ll34TcV0QeE1V5ZnCn/ySmHQdg4Pt+0erafi3qW
    nvnRgUHRF9O3zLVv5DmpGdz+yyrrJAHYyHuPM
    EOuOUepdTsfuw8UmoRUYb86OwL7qi2YFfVA5
    bUtmjujWwWawzb+aagZZhVCNLipYtF6cCtRDS9
    /jo3Z7nVhzgV40RfEhWsgnS24TJMoPsk3PgA+nA
    XWv2voULAaG282GnZ6OEkMEfCi0P65fh+Y4ZJti
    cmusEZGcFkx2niMD8nyG6pQx08BZsiSXJnKLNU
    hJF6O7zahuA/Ew=

  • Import parameters

    Click on "Import parameters" in "File" menu or press "Control + I". With the form that opens you can import the parameters using two ways:

    1. Click on "Examine" so that a dialog box would be opened and you can search the file of the exported parameters.

      Import parameters form - File

    2. Enter the line of the parameters in the text area and click on "Import".

      Import parameters form - Line

    The corresponding image will be calculated in a new canvas.

  • Download parameters

    Click on "Download parameters" in "File" menu to access the online parameters library of the users. Within the library, search for images that are interesting to you and download their parameters to work with these images.

Learn more...
Be aware that, when exporting with the option "Only parameters", the previous content in Windows' clipboard is lost, thus it is replaced with the new parameters.

Parameters files can also been imported by dragging and dropping them in the EFF working area.

 

VIEW THE JULIA SETS OF A FRACTAL

Open the "Julia viewer" from the "View" menu or press "Control + Alt + J". If the "Active canvas" is compatible, this viewer shows the Julia sets that compose the image.

* The "Julia viewer" is only compatible with fractals based on "Mandelbrot's method", excluding the special fractals.

To view the Julia sets move your mouse over the canvas.

Julia viewer

In order to calculate the Julia set that is sown in the viewer press "J" key and click over the canvas without moving the mouse.

Learn more...
Mandelbrot's drawing method represents a map of all possible Julia sets. Corresponding Julia sets to inner Mandelbrot are closed, while corresponding to outer Mandelbrot are opened.

 

CREATING MAPS OF JULIA

* Maps of Julia are not available for special fractals and are only compatibles with fractals based on "Mandelbrot's method".

Open the "Julia maps" designer from the menu "View" or pressing "Control + Alt + M".

Maps of Julia designer

(The box "Adapt Julias" centres and fits in its cell every Julia set)

Adjust the number of cells and press "Start". Save the resultant image once the process ends.

Learn more...
Julia maps are made of Julia sets ordered suitably so a map equivalent to a graphic obtained with "Mandelbrot's method" is shown.

 

CREATING CELLULAR NOISE

To create cellular noise, EFF locates randomly a set of points which are known as "Cells" and then applies the "Voronoi Diagram" to the set to colouring the plane.

Open the Cellular noise designer from the menu "View" or pressing "Control + Alt + C".

Cellular noise designer

In order to set the drawing process:

  • Choose the number of cells you want to use.

  • Adjust the distance of reference for the calculation. The value 1 is the distance to the farthest cell and the polygons will be drawn with more definition.

  • Choose one of the colouring methods available:

    1. To use a single colour check the box "Colour" and select it.
    2. To use a palette, uncheck the box mentioned in the previous point and then select a palette in the combo box.

Finally, choose the aspect ratio and the size you wish to the final image (zone 1 in the image) and then press the button "Start".

At any time, during calculation and once completed, the colours may be inverted. To do this, press the button "Invert".

The image can be saved when the process finishes.

 

CREATIG STEREOGRAPHIC PROJECTIONS

* The Stereographic projection is not available for the special fractals Bifurcation and Buddhabrot.

To draw the projection, EFF locates a Riemann Sphere on the fractal and then calculates how it is reflected on its surface.

Open the "Riemann Sphere" designer from the menu "View" or pressing "Control + Alt + N". The sphere previews will be drawn automatically if the "Active canvas" is compatible.

Stereogrphic projections designer

Adjust the general options: "Background" colour, "View" type, and output "Size". Then, select one of the following processes:

  • Generate images (zone 1 in the image)

    This process generates an image with the set of selected views, and one independent image per each of them. To do this, check the views you wish and then press the button "Start". The images can be saved when the process finishes.

  • Generate seguence (zone 2 in the image)

    This process generates a sequence of images of the spheres' elevation (central preview). To do this, set the following parameters:

    1. Initial illumination: start location of the light focus.
    2. Focus spins: number of spins that give the focus and the direction.
    3. Sphere spins: number of spins that give the sphere and the direction.
    4. Length: length in seconds of the sequence.
    5. FPS: number of frames per second.

    Then press the button "Start". While the process is running, the frames will be saved in the images folder of the application, inside a specific subfolder for the process. You will be able to open the images' folder when the process is finished.

 

CREATING KALEIDOSCOPIC IMAGES

Open the Kaleidoscopes designer from the menu "View" or pressing "Control + Alt + K".

Kaleidoscopes designer

This designer has an area that allows to customize the triangle that is taken as a pattern to draw the kaleidoscopic image, and another one that allows to customize the final image (zones 1 and 2 respectively).

In the combo box "Image" choose "B.DEFAULT" in order to create a kaleidoscopic image from the "Active canvas" or choose a value to create it from imported images in EFF.

In order to customize the triangular pattern:

  • Modify its size with the adjust control "Size".

  • Modify its position with the left button of your mouse over the preview.

In order to customize the final image:

  • You can apply the "Tube" effect with the wished colour.

  • You can show the triangular "Divisions" with the wished colour.

Finally, choose the aspect ratio and the size you want for the final image (zone 3 of the image) and then click on the button "Save image".

The button "Save texture" allows saving the basic image that serves to fill in the areas of any size.

 

CREATING DIFFUSION-LIMITED AGGREGATIONS

The aggregate is achieved by a particles liberation that takes random paths until they collide with something that stops them. EFF allows to set a seed in order to make the aggregate grow around it.

Open the aggregation designer from the "View" menu or press "Control + Alt + G".

Aggregates designer

In order to set the aggregate process:

  • In the combo box "Seed", chose the image you wish. Then, you can change its position with the left button of your mouse over the preview.

  • Modify its size with the adjust control "Size".

  • Select an available colouring method in the combo box "Method".

    1. BORDER: it colours the image according to the distance between the particle and the canvas borders.

    2. SEED: it colours the image according to the distance between the particle and the seed borders.

    3. MIX: this is a mix between the two previous colouring types.

    Border, seed and mix aggregates
  • Select an available palette in the combo box "Palette".

  • Choose the aspect ratio and the size you want for the final image (zone 1 of the image). The process may take some time depending on the selected size, but the "Aggregates designer" can be closed without interrupting itself.

Then, press the "Start" button in order to start the process. It will end by itself when all the canvas edges are closed and no more particles can access, but the background colour can be selected and the image can be saved at any time. To do this, check the box "Background", select the colour and then press the button "Save image".

 

CREATING SIERPINSKI DESIGNS

Open the Sierpinski designer from the "View" menu or press "Control + Alt + D".

Siepinski designer

In order to set the algorithm, adjust the iterations number and select an available drawing mode: "Triangle" or "Carpet".

To customize the image choose the colours you want for the inside and outside zones of the fractal.

Finally, choose the size you want for the final image and then click on the button "Save image".

 

CREATING PYTHAGORAS TREE

Open the Pythagoras designer from the "Vew" menu or press "Control + Alt + Y".

Pythagoras designer

To set the drawing algorithm:

  • Adjust the iterations number. A bigger number of iterations will produce more branches.

  • Adjust the value of the variable angles of the right triangle. This causes the tree to tilt to one side or the other.

  • Adjust the trunk height. Its maximum value will depend of the size of the tree.

  • Adjust the size of the tree.

  • Activate the "Zigzag" mode to create a pointy tree or inactivate it to create a rounded tree.

To customize the image choose the colours you want for the inside and outside zones of the fractal.

Finally, choose the size you want for the final image and then click on the button "Save image".

 

AUTOMATE PROCESSES WITH TASKS

* Tasks are not available for the special fractals.

Open the tool "Tasks" from the "View" menu or press "Control + Alt + T". This tool has a tab page per task with the adjusting controls for its parameters and a common area for all tasks that allows to fix the precision of the adjusting controls (zone1 in the image).

Tasks form

EFF 7.7 version includes the following tasks:

  • Iterate: it increases or decreases the iterations number.

  • Zoom: it performs a progressive zoom, positive or negative.

  • Exponent of Z: it increases or decreases the exponent of the variable "Z".

  • Rotate: it increases or decreases the image rotation angle.

  • Palette scrollyng: it scrolls the colours of the palette.

  • Initial Z: it increases or decreases the initial value of the variable "Z".

  • Center: it scrolls the fractal horizontally and vertically.

  • Julia: it modifies the "Real" and "Imaginary" components of Julia's constant "C".

  • Distortion: it modifies the "Real" and "Imaginary" components of Distortion constant "D".

  • Relaxation: it modifies the "Real" and "Imaginary" components of Relaxation constant "R".

  • Orbit trap opacity: it increases or decreases the opacity of the orbit trap.

  • Orbit trap size: it increases or decreases the size of the orbit trap.

  • Orbit trap scrolling: it scrolls the orbit trap.

Not all tasks are supported with all fractals, thus some of them are shown as "disabled" depending on "Active canvas".

Click on the "Start" button in order to associate the task tool to the "Active canvas". Then, adjust the parameters and check the boxes of the tasks you would like to perform. This will modify progressively the parameters and will calculate a new image of the fractal every time.

Uncheck the box of a task if you would like to stop it, and click on "Stop" button when you wish to disassociate the canvas.

Learn more...
The "Tasks" tool can only associate to one canvas every time (all exploring functions relay disabled during the association).

A task can stop itself if any of the parameters reaches invalid values with the type of fractal loaded in the canvas.

The "Decimal" adjust allows to select the decimal position that will vary in the parameter value when it is modified through its own adjusting control (it only works over tasks highlighted in blue).

A task can be used combined with the option "Save image changes automatically" of the "Options" form in order to get images, like movie frames, for building a video or animation using an external application.

 

VIEW INFORMATION ABOUT THE FRACTAL

Open the tool "Information" from "View" menu or press "Control + Alt + I". This tool shows up information concerning the "Active canvas".

Information form 1   Information form 2

The available information is the following:

  • Coordinates: visible area

    It shows the coordinates of the area of the fractal represented in the image.

  • Coordinates: central point

    It shows the coordinates of the point of the fractal corresponding to the centre of the image.

  • Coordinates: mouse pointer

    It shows the coordinates of the point of the fractal corresponding to the pointer location.

  • Dimensions: full set

    It shows the approximate diameter that the full fractal should have to view the selected area. It also compares this value with the size of a real object.

  • Dimensions: visible area

    It shows the approximated diameter of the fractal area being viewed. It also compares this value with the size of a real object.

  • Dimensions: image

    It shows the printing dimensions of the image and its aspect-ratio.

  • Zoom limit:

    It shows the zoom level of the "Active canvas" in a progress bar. It is located over a background that changes its colour in relation to three zoom levels: low (green), medium (amber) and high (red).

  • General information

    It shows the type of fractal, the identifier number of its window and its comment.

You can also view the formula used during the drawing of the "Active canvas". To do this, open the "Formulas viewer" from the "View" menu or press "Control + Alt + R".

Formulas viewer

Learn more...
The window identifier allows you to locate the subfolder corresponding to the canvas within the images folder.

 

HIBERNATION OF PROCESSES

Another important feature of EFF is that it allows closing the application at any time without losing the state of calculate of the images that are still to be finalized. The next time you start the application it will display an informational message giving the possibility to open the tool "Hibernated processes", where you can resume the process from the point where they left. To do this, choose the hibernation you wish and click on "Continue" button. This tool can also be open from "View" menu or press "Ctrl + Alt + H".

Hibernated processes form

Learn more...
The calculation of certain images can be a slow process according to the fractal characteristics, the image size or the "Anti-aliasing filter" applied. In occasions like these you may need to close the application and it is then when the hibernation of calculation avoids losing the work previously done.

 

TIPS

To make a good use of EFF check tips (spanish).

EFF has a web desktop with direct access to www.fractfinder.es. The web desktop integrates itself within the main frame of the application in order to improve the experience, allowing interacting between information and EFF. You can open the web desktop in "View" or press "Control + Alt + W".

Learn more...
Whenever the web desktop is selected, shortcuts keys would not be available in order to access the functions of "File" menu nor of "Edit" menu. If you want to use this, activate any other form of the application without closing the web desktop.



Translated to English by Vanessa JH


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