NAME
    App::GUI::Harmonograph - drawing with 4 lateral and 2 rotary pendula

SYNOPSIS
    1.  read this POD page

    2.  start the program in shell: > "harmonograph"

    3.  move knobs in tabs and observe preview sketch reacting until the
        drawing is interesting

    4.  push *Draw* (right below drawing board or "Ctrl+D" or "Alt+D" or in
        Image menu) to produce a full image

    5.  choose in menu *"Image"* > *"Size"* size of output image in pixel
        and right below also output format. Then select there *"Save"* (or
        push "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. Load it from there later to restore settings for
        further tweaking.

    After first use of the program, a config file will be created under
    *~/.config/harmonograph* in your home directory. It contains mainly
    stored colors and dir entries that tell the app from where to load and
    store files. You may change it manually or deleted it to reset defaults.

DESCRIPTION
    An Harmonograph is an apparatus with several connected pendula, creating
    together spiraling pictures :

    This is a cybernetic recreation of an Prof. Blackburns invention with
    several enhancements:

    *   fourth pendulum is a rotation of drawing board

    *   pendulum five and six create an epicycle

    *   pendula can oscillate at none integer frequencies

    *   separate complex amplitude and frequency damping in 8 flavours

    *   draw lines or dots with changeable size, density and probability

    *   complex color rainbows with up to 10 color, 3 types of color change
        patterns and with changeable speed and polynomial dynamics

Mechanics
    The classic Harmonograph is sturdy metal rack which does not move while
    3 pendula swing independently. Let us call the first pendulum X, because
    it only moves along the x-axis (left to right and back). In the same
    fashion the second (Y) only moves up and down. When both are connected
    to a pen, we get a combination of both movements. As long as X and Y
    swing at the same speed (frequency), the result is a diagonal line.
    Because when X goes right Y goes up and vice versa. But if we start one
    pendulum at the center and the other at the upmost position we get a
    circle. In other words: we added an offset of 90 degrees to Y (or X).
    Our third pendulum W moves (wobbles) the paper in circulating manner
    around its center (but not rotating, so a dot in the left corner will
    always left). If both circular movements (of X, Y and the one of W) are
    concurrent - the pen just stays at one point over the paper and paints
    only a dot. If both are countercurrent - we get a circle. Interesting
    things start to happen, if we alter the speed of of X, Y and W. Than
    famous harmonic pattern appear. And for even more complex drawings I
    added R, which is not really a pendulum and not part of the original
    Harmonograph, but an additional rotary movement of the paper around its
    center. I added even 2 more pendula (E and F which are also lateral like
    X and Y), which draw an epicycle around the point where the dot would be
    normally drawn.

    The pendula out of metal do of course fizzle out over time, which you
    can see in the drawing as a spiraling movement toward the center. We
    emulate this with two damping factors: one for amplitude/radius and one
    for the frequency (speed). The radius or ampitude of Pendulum R is
    special and allows you to zoom in or out in case you wish to do so.
    Normally this is not necessary, since the program autoadjusts to the
    settings, so that the picture is always fully visible and as big as
    possible.

GUI
    The general layout of the program has three parts:

    1   In the left upper corner is the drawing board - showing the result
        of the Harmonograph.

    2   The whole right half of the window contains the settings, which
        guide the drawing operation. These are divided into six tabs, which
        will be explained in detail below.

    3   In the lower left corner are two rows of buttons. The first row
        contains only the progress bar and the *Draw* button for drawing a
        full picture. The progress bar remains white whily previe sketches
        are shown. But when a full picture is drawn, then it gets filled
        with colors that reflect the color flow used while drawing.

        The second row of buttons allow the mass production of graphic files
        without using the menu. That is explained in detail under
        "Commands".

    Please mind the tool tips - short help texts which appear if the mouse
    stands still over a widgets. Also helpful are messages in the status bar
    at the bottom - on bottom left regarding current state of the image and
    bottom right about state of the settings. Settings are all the
    parameters that guide the drawing. You change them via widgets controls
    on the right side. They can be saved and loaded from a file via the
    settings menu. Configuration are the general settings of this program,
    which are mostly saved colors and paths were to store images and
    settings.

    When browsing the main menu, help texts about the highlighted item also
    appears in the status bar. The Menu can be completely navigated with the
    keyboard. Just hold Alt and use the direction keys (up, down, left and
    right) or the highlighted letters. When holding the Alt key you can also
    see which Alt + letter combinations trigger which button.

  Pendulum
    Each of the first three tabs contains the settings of two pendula. The
    first tab holds the lateral or linear pendula: X (left right movement)
    and Y (up and down). The second tab shows settings of the epicycle
    pendula E (left right) and F (up down). They also just move in x or y
    direction, but they swing not around the center of the image but around
    the point, where the pencil would have been. The third tab allows you to
    tweak the pendula W (wobble) and R (rotation). W moves the center of the
    paper beneath the pencil in a rotating manner whereas R rotates the
    paper around its center. Each of these 6 pendula have the exact same
    settings which behave all the same, except radius of R, which works as a
    zoom.

    In the left upper corner of each pendulum settings is a checkbox to
    activate or deactivate the pendulum - good to see the pendulums part in
    the pen movement. The rest is organized in 8 rows, which can be divided
    into 3 parts. Row 1 - 4 are about the pendulum frequency in Hertz. Row
    five allows you set the starting point (offset) and the last 3 rows are
    about the radius or amplitude of the pendulum mirroring the rows 1, 3
    and 4 because the work exactly the same way just not for the frequency
    but the radius parameter.

    Row one sets the whole number part of the frequency. This is the part
    you need to generate to generate the famous images which are based on
    integer rations. You can either use the slider the + an - buttons or
    insert a number into the text field (which is true off all slider combo
    widgets). Behind the slider combo in row one is a drop down menu which
    lets you choose a natural constant like Pi or Phi. It gets multiplied
    with the frequency. This allows you to explore the nature of these
    famous constants. Among the constants are also the natural numbers 1, 2
    and 3 in case you need to crank up the frequency up to 300.

    The second row enables you to set values with three decimals. If you for
    instance choose a base frequency of 5 and dial in 15 in the second row,
    the actual frequency will be 5.015 times the natural constant. Behind
    the slider are two checkboxes. One to additionally invert (1/x) the
    frequency value and one to flip the pendulum direction (f = -f).

    The third row lets you dial in a damping value which makes the pendulum
    each round slower (bigger value -> more damping). Behind it is a
    selector. If its on minus the damping will be same each round but set on
    "*" the damping will be proportional to the frequency. Still behind it
    is a checkbox. When selected the frequency is allowed to become negative
    by damping.

    The fourth row is about daming acceleration or with other words, how
    much the damping changes from dot to dot. Beside the c value you have
    this time four types of acceleration. Minus and times work as before and
    plus and divided by are just their opposite.

    The fifth row has a slider that sets the starting position of the
    pendulum along its expected track. If the slider is on max you move the
    pendulum a quater rotation ahead. To add another quarter check the box
    left beside it. The last box adds another half rotation. This allows you
    to flip or mirror the image in meaningful ways.

    The sixth row mirrors the first but with 2 distinctions. Its not about
    integer values but percentage values of the original pendulum length.
    This length will be calculated by the program for opimal display. Thi
    slider helps you only to change the proportions of the amplitude towards
    the other pendula. Natural constants are also here available as a factor
    and behind the on the most right is a button to reset the radius to 100
    percent.

    The seventh row is the amplitude size, which simple allows to make the
    picture larger or smaller depending if the pendulum left the frame or
    doesn't move enough. As with reqency, also the amplitude can be damped
    over time and this damping can accelerated.

    Row eight and nine are exact copies of row three and four, they just
    affect the radius / amplitude.

  Functions
    This tab lets you meddle with the equations that compute the mechanics
    of a pendulum. Because all ten rows are built the same I will explain
    only one. For instance the X pendulum has only influence on the x
    coordinate of a dot, it is computed: "x = radius * cos (time)". The
    first selector allows you to swap out the cosine function. Instead you
    could get sine, tangent, cotangent, secant, cosekcant and the hyperbolic
    twin of the already mentioned functions.

    The second selector has five options: "= + - * /". If you choose the
    first (equal sign) your time variable will be just swapped out with
    another variable. The other four option describe the operation that will
    be applied upon you time value. So e.g. if you select plus the resulting
    formula will be "x = radius * cos (time + (...))". The dots allude to
    whatever you will choose with the next three selectors.

    Selector three and four are just factors. They contain natural numbers
    and natural constants you can multiply the variable with. And last not
    least selector five holds the variables time frequency and
    radus/amplitude of each pendulum. This allows you for instance add the
    (always) current pendulum frequency of pendulum W to the time value of
    Pendulum X resulting in unpredictable shapes. There is lot to explore.

    Pendulum W affects the x and y coordinate, hence it has two rows for
    each case. Even more special is "Pendulum" R - the rotation movement of
    the paper. This is computed by an ordinary 2 x 2 rotation matrix (we are
    in 2D). Each cell of this matrix has here its own row. Its R_11, R_12,
    R_21, R_22. But if you not sure just hover with the mouse and get the
    hints.

    The very last row is different and contains only one switch that will
    determine if W or R pendulum is applied first. Default and what is also
    more comprehensible is that R is apllied first. But the arstist in you
    might can choose here differently.

  Visual Settings
    Due to the section headins, this tab is self explanatory. First choos if
    you want to paint dots or connect them. Please not that pen thickness of
    one is very thin and you might not see any dots in that setting. The pen
    style is more of an gimmick. Most useful are solid and dotted lines. The
    dot density allows you to juggle two extremes. Low density makes for
    fast drawn lines and dots but also pointy curves. So you might want to
    raise the value for smooth curves. The fine tuning of dot density makes
    only sense if you draw dots, becasue even a slight change can produce
    very different dot pattern. The line length is in seconds in minutes so
    you can understand their proportion to the frequencies, which are in
    Hertz (rotation / second).

    The last section on this tab is about the color change or color flow.
    You have 4 types and according to the current type only the widgets
    which have an impact are enabled. When flow type *"no"* in on, you paint
    only with color number 1 and the progress bar in the left lower corner
    will have one color. It allows you always to track which color rainbow
    you actually chose. But its only visible if you make a full picture. So
    push the Draw button. When color flow type *"one_time"* is active, you
    have to also select how many colors you like. And if you e.g. choose 3,
    your rainbow will go from color 1 to color 2 to color 3. And it will be
    spreat of the whole painting time, depending how much you selected. The
    dynamic option tells something about how the change from one color to
    the next will look like. Positive values bend the rainbow toward the
    start of a gradient and negative toward the end. So with a dynamic of 5
    the rainbow will linger on the starting color for a long time and will
    then change faster and faster. The color flow type "alternate" moves
    from color one to two, three and so forth and then backwards back to one
    and then again forward as long as your chosen painting time permits.
    Regulate the color change speed with the "Speed" slider. For extra slow
    color changes hit the "Invert" checkbox. Than high speed values will
    make it extra slow. The last color flow type is *"circular"*. Here you
    go again from color one to the selected last color and from there
    directly to color one. This round will repeated as time permits.

  Colors
    This tab is just for choosing the available colors. There are alway ten
    colors visible, but colors with a "x" below are currently not in use.
    This tab page has five sections which will be explained from top to
    bottom.

    The first section is about loading saving sets of colors, so you don't
    have to dial in your favorit arrangements every time. Just choose your
    set via the drop down menu or browse there with the arrow buttons. A
    preview will be shown below th e selector. Then press load and the
    selected set will be loaded into the currently used colors in the middle
    of the page. If you want to tweak a set you can do so color by color (as
    shown below) and then save (overwrite) the color set which is currently
    displayed. Or press new to create a new color set that contains the
    currently displayed colors. You will be asked to give it a name that is
    not already taken. And caution with the "Del" button. If you press it,
    the currently displayed set is gone.

    Below that is the second section with buttons that trigger color
    functions. This helps you to compute related colors. To better
    understand their working check the module Graphics::Toolkit::Color. If
    you push the "Gradient" button that a smooth color gradient will be
    calculated between the leftmost color number one and the currently
    selected color. The value after the button skews the gradient towart the
    start (positive values) or the end (negative values). The "Complement"
    button also computes colors between color one and the current but these
    will have equally distanced hues but the same brightness and saturation.
    The text fields after the button allow you to skew the brightness and
    saturation. Behind that, at the rightmost position are two buttons to
    move the currently selected color around.

    The third section below that displays the colors than can be used to
    draw the picture. They are ten colors, numbered from left to right.
    Below each color field there is a second rectangle showing the status of
    the color. If this rectangle is empty, the status is normal (used). If
    it's crossed out, them the color is inactive because in the visual
    settings you choose to use less than ten colors. The third option is
    selected color. To select a color, just click on the rectangle
    displaying that color or the status rectangle below. Then the status
    will show an arrow down.

    This means the section below displays the values of this color. And the
    values can also be changed there. First your have the *red* (R), *green*
    (G) and *blue* (B) values of the RGB color space. below that are ones of
    HSB: *hue*, *saturation* and *lightness*. These are more meaningful to
    the human mind. At the right end of each row that shows amd changes one
    color value is a button with a question mark. Push that to randomize
    this one value.

    The last and fifth section is analogous to the first one. It is a store
    for your favorite single colors. Just load and safe the currently
    selected color via the buttons. Be again cautious with the "Del" button.

  Commands
    In the lower left corner are two rows of command buttons. All other
    commands are in the menu.

    The lower left part of the window contains buttons in two rows. The
    upper row is just for drawing the complete image. It has a progress bar
    and the draw button. If the progress bar is white, you see just a sketch
    drawing - a preview of the full image that can be computed fast enought
    to react to all setting changes. If you push the draw button (or
    <Ctrl>+<S>), you will get a full image and the progress bar has the
    color of the drawing and also can show you the color progression over
    time, so you can see, which are the early and the later parts of the
    drawing.

    The second button row is for easy mass production of drawings. The three
    text fields are combined the parts of the file path. The first text
    field is naturally the directory where the files get saved. You can
    change it by pushing the *Dir* in front (left) of the text button and
    use the then opening Dir-Dialog to select another directory. The second
    text field holds the base file name, which has to be inserted by
    clicking on in and typing. The third text field is the file number and
    is readonly. That counter increments automatically when a file is
    generated. The complete file path is <dir>+<base
    name>+'_'+<counter>+<file ending>. The file ending is *.ini* for setting
    files and *.jpg* or *.png* or *.svg* for image files. The exact ending
    depends on what is the current configuration set in the image > format
    menu. Lets say your directory is "/home/user/images/h" and the base file
    name is beauty. If there is already a file
    "/home/user/images/h/beauty_4.png" - the program will detect that and
    set the counter to 5. You can play with the settings and than (no matter
    if there is currently a complete drawing or not) push the *Save* button
    to produce a complete drawing into "/home/user/images/h/beauty_5.png".
    If you push the *INI* button you safe the current settings into
    "/home/user/images/h/beauty_5.ini". This file can later be loaded via
    settings menu to restore the current state of all buttons in the tabs.

  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. I recommend giving them the file ending ".ini" for transparency
    reasons. A submenu 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 only sets the preferred format, which is the
    format of the serially save images by the command buttons in the left
    lower corner. The preferred file format is also the first wild card in
    the save dialog. Above that is another submenu for setting the image
    size.

    The third menu has only one item to oben the *about* - dialog, where you
    can see which perl, Wx and other versions you are currently using.

SEE ALSO
    App::GUI::Cellgraph

    App::GUI::Juliagraph

    App::GUI::Sierpingraph

    App::GUI::Spirograph

AUTHOR
    Herbert Breunung (lichtkind@cpan.org)

COPYRIGHT & LICENSE
    Copyright(c) 2022-25 by Herbert Breunung

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

