NAME
    App::GUI::Juliagraph - drawing Mandelbrot and Julia fractals

SYNOPSIS
    1.  read this POD

    2.  start the program (juliagraph)

    3.  move knobs and observe how preview sketch reacts til you got an
        interesting image

    4.  push "Draw" (below drawing board or Ctrl+D) to produce full
        resolution image

    5.  choose "Save" in Image menu (or Ctrl+S) to store image in a PNG /
        JPEG / SVG file

    6.  choose "Write" in settings menu (Ctrl+W) to save settings into an
        INI file for tweaking them later

    After first use of the program, a config file *~/.config/juliagraph*
    will be created in you home directory. It contains mainly stored colors,
    color sets and dirs where to load and store setting files. You may also
    change it manually or deleted it to reset defaults.

DESCRIPTION
    Mandelbrot (first thee) and Julia fractals (second three following) are
    just mathematical diagrams, showing you how iterating the equation
    "z_n+1 = z_n ** 2 + C" behaves in the complex plane. The pixel
    coordinates are taken as input and the count of iterations it took to
    exceed the stop/breakout value decide which color this point will
    painted in. In Mandelbrot fraktals the coordinates will be put into the
    variable C and in Julia fraktals into the variable z_0 (initial values
    of the iterator variable).

    This program has additional capabilities/options:

    *   choosable exponent above z_n

    *   a linear part of the term making the formula into: "z_n+1 = z_n **
        EXP + L * z_n + C"

    *   choosable stop value and stop metric

    *   free selection of colors

    *   many option to map th colors onto iteration result values

GUI
    The general layout is very simple: the settings (which define the
    fractal) are on the right and the drawing board is left. The settings
    are devided into several thematic tabs.

    Please mind the tool tips - short help texts which appear if the mouse
    stands still over a button. Also helpful are messages in the status bar
    at the bottom that appear while browsing the menu.

  Form
    The content of the first tab are the settings that define the shape of
    the fractal. It also allows you to scroll and zoom into your region of
    interest.

    This page contains 7 complex widgets, which need a little more
    explanation. They stretch over a row and have three parts. The leftmost
    part is a text field which you could change directly. In cases when
    pasting or typing special values into it they may be used, but in most
    other cases it is more convenient to use the other parts, since every
    value change will triger a new sketch drawing, which is not always fast.
    On the rightmost is a slider, which allows you to dial in a value. This
    value will be added or subtracted from the value in the textbox if you
    push the buttons in the middle part.

    The first row on this page has two widgets. The first is a radiobox that
    lets you choose between Julia and Mandelbrot fraktals. The other is a
    combobox that lets you set the exponent in the iteration formula (see
    "DESCRIPTION"). These are the settings that change the shape most
    fundamentally.

    Next are the inputs for the values A and B these are the real and
    imaginary parts of a complex constant. In a Julia fraktal this constant
    is added after each iteration. In the Mandelbrot fractal it will provide
    the starting value of Z.

    Below that are the values C and D, which are real and imaginary parts of
    a factor. During each iteration the product of this factor with the
    iterator variable z will be added like the constant.

    Below further are the X and Y coordinates of the center of the image.
    Changing these will move the visible part of the fractal left/right or
    down/up. Please note that these values are relative and if you zoom in,
    they will be become smaller.

    The second lowest input is the zoom factor. It is greater the more you
    zoom in.

    The lowest row contains two choices. First the stop value. If the
    iteration variable has a greater value than it - the iteration stops.
    Because we compare an complex iteration value with a real number, we
    compute the absolute value of the iteration variable (displayed by
    "|var|"). But other metrics are possible. Just keep in mind x is the
    real part of the iteration variable Z and y is the imaginary part.

  Color Mapping
    On the second tab we have three rows of settings which determine how the
    selected colors will be applied.

    The first checkbox selects if we use the colors at all or just the
    default grey gradient. The combobox in the first row let you pick how
    many of the selected colors will be used. If you choose for instance 6,
    the first six (1..6) are used to display the fraktal, plus of course
    black as the background color for the area where the iteration variable
    never reaches the stop value. Never in this context mean the maximum
    available amunt of iterations as computed by the product of the numbers
    shown on this page except *Dynamics*.

    The second row defines how we proceed from one color to the next. If for
    instance *Gradient* set to 5, there will be 5 additional colors between
    each of the selected colors, to make the transition smoother. If
    *Dynamics* is set to 0, this transition will be linear. Otherwise it
    will tilt into one or the other side.

    The third row has two more settings which will influence the shape of
    these gradients. By setting the *Grouping* value higher than 1 you
    stretch the gradient by a factor. If for instance *Grouping* is set to
    three, three neighbouring areas which normally would have three
    different colors will have the same color and just the next, forth area
    will contain the next color. The *Repeat* value also multiplies the
    number of used colors. As soon the painter runs out of colors it will
    take the first again and repeat this process the ordered amount of
    times.

  Colors
    This page helps you to select the color that will be used to paint the
    fractal. Only the background color is currently fixed to black. You can
    see these colors in the middle section named "Currently Used State
    Colors". If you click on one - it will be selected which you can see
    from_rgbthe arrow below the selected color.

    In the section below named "Selected State Color" you see the values in
    RGB space and HSL space of the selected color. Yan change any of them
    directly by slider, typing them in or pressing the plus and minus
    buttons.

    The "Color Store" in the last row allows you store the selected color
    for later reuse (just press save and type in its name). With the combo
    box or the arrow buttons you can also select there a color and press
    load to chhose it as the new currently selected color. Press there
    Del(ete) to delete the visible color from the store.

    Analogues to that there is a color set store in the first row of this
    page which enables you to store and load all currently used colors at
    once. Please use there the *New* button to create a new color set to
    avoid overwriting the currently seleced color set, when pressing *Save*.

    The second row contains some color set functions to create gradients
    between the leftmost and selected color or to compute colors that are
    complementary to the selected.

  Menu
    The upmost menu bar has only three very simple menus. Please not that
    each menu shows which key combination triggers the same command and
    while hovering over an menu item you see a short help text the left
    status bar field.

    The first menu is for loading and storing setting files with arbitrary
    names. Also a sub menu allows a quick load of the recently used files.
    The first entry lets you reset the whole program to the starting state
    and the last is just to exit (safely with saving the configs).

    The second menu has only two commands for drawing an complete image and
    saving it in an arbitrary named PNG, JPG or SVG file (the file ending
    decides). The submenu above onle set the preferred format, which is the
    format of serial images and the first wild card in dialog. Above that is
    another submenu for setting the image size.

    The third menu has only a dialog with some additional information of
    version numbers and our homepage.

SEE ALSO
    App::GUI::Cellgraph

    App::GUI::Harmonograph

    App::GUI::Sierpingraph

AUTHOR
    Herbert Breunung (lichtkind@cpan.org)

COPYRIGHT
    Copyright(c) 2023 by Herbert Breunung

    All rights reserved. This program is free software and can be used and
    distributed under the GPL 3 licence.

