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 or *Draw* in *Image*
        menu) 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 by editor or delet it to reset configs to default.

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 values at the
    pixel coordinates or some chosen constant is taken as input (z_0) 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:

    *   iteration formula with up to four monomials

    *   choosable exponent and factor for each of them

    *   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.

  Constraints
    The controls of the first tab are the settings that define most of the
    math, but not the higher polynomials. The page is divided from top to
    bottom in 4 sections for fractal type, scrolling and zooming, iteration
    constant, and stop condition.

    The first section allows you to set the fractal type: *Mandelbrot*,
    *Julia*, of something in between (option *Any*). If you choose
    *Mandelbrot* the complex value of the current dot in the coordinate
    system becomes C in the above mentioned formula and the complex constant
    of section 3 is the starting value Z_0. With *Julia* both these values
    switch their usage and with *Any* you are free to choose their usage.
    You could discard them of even use them as factor of the higher
    monomials.

    The second section allows you to zoom in and out and to select the
    central coordinates of the visible cutout. For this it has a three
    partial_hash_deformat widget, which need a little more explanation. The
    leftmost part is a text field, in which you could change the numbers
    directly by pasting or typing. The ladder is not recommended, since
    every change will trigger a redraw of the fractal preview. Instead of it
    use the slider on the right and dial in the amount you want to see the
    value on the left changed. If you hover the mouse over the slider, it
    will show you the amount. Then push the buttons in the middle to add or
    subtract the dialed in value. In the same way you can choose X and Y
    position to move the visible window.

    The third section works the same, but helps you to set the a complex
    value, that will be used in the manner you have set in section 1. Just
    note *A* is the real part of the constant and *B* is the imaginary part.

    The fourth section contains two choices. First the stop value. If the
    iteration variable *Z* has a greater value than it, the iteration stops.
    Because we compare an complex iteration variable 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.

  Polynomial
    The second tab contains 4 identical sections which also work the same.
    Each of them stand for a monomial of the iteration equation, but only if
    the checkbox *On* is marked. A second checkbox allows you discard the
    complex factor below which will be set in the same way as the constant
    on the first tab/page. (Read there how to use the slider button widget.)
    The maybe most important control of an monomial is the exponent, which
    you select on the right side of the first row. A *Mandelbrot* or *Julia*
    fractal is usually computed just with "Z_n+1 = Z_n ** 2 + C", but higher
    exponents are gateways into other worlds with more symmetry. You could
    select via this page a term like "Z_n+1 = F_1 * Z_n ** 5 + F_2 * Z_n **
    2 + C" An exponent of one will just add a linear component which usually
    smears the fractal in sometimes interesting ways. An exponent of zero
    will make the factor of this monomial into a constant, same as one on
    the first tab. If you you have several monomials with the same exponent,
    the factors will be multiplied.

  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.

