PascGalois JE Help: 2-D Cellular Automata Image Tab
The Image Tab
Once all of the options are set you are ready to graph the automaton.
Simply select the Image tab and click the refresh button, the one in the
upper right of the tab. Once you do you will see something like the following
image. Here we are using a finite automaton over Z5.
The tab is fairly simple but it has many options in the menu system. We will discuss
the layout and mouse options before going into each menu option. When exploring these
images the main thing you as a user want to do is alter the color schemes to bring out
information on the underlying structure of the group. Since regraphing the image can take
some time and you will most likely be doing several color changes to achieve the desired
result we do not regraph the image after every change you make. Hence, when dealing with
color changes to see the change you will need to click on the refresh button in
the upper right. The layout of the tab is simple. The image is to the left and the
element/color correspondence is on the right. There is a menu at the top and a status
bar at the bottom. Directly above the color correspondence is a color scheme selector
drop-down box. Each child window may have as many color schemes as you would like.
The divider between the image and the element/color correspondence is movable.
There are three viewing modes for two-dimensional automata. One is a
three dimensional rendering of the stacked levels (time-steps) of the automata.
This view is done in the external 3-D Viewer. The other two modes are an
element viewer for a specific time-step and a probability density viewer which
graphs the probability that a cell contains an element from some selected subset
of a finite group.
The Time-Step Viewer
When you move the mouse over the automaton the position you are pointing at and the
value of the element at that position are displayed in the status bar and if you hover
for a few seconds over the automaton the position and element are also displayed
as a tool tip close to the cursor.
If you double-click on an element in the image or on an element in the element list
a color chooser dialog box will appear allowing you to select a new color for that
element. Remember that you will need to select the refresh button to see the color
change.
If you right-click on the image or on an element in the element list a popup
menu will appear with the options to change the element's color, to make the
element transparent and to copy and paste a color. If you select to change
the element's color the same
color chooser dialog box will come up. If you select the transparent color
option then the color in the element list for the selected element will be
a box with an x through it, signifying a transparent color.
When the graph is refreshed the background color will show through the transparent
elements. Copy and paste will simply copy and paste the color to and from the
system clipboard.
Before moving onto the menu options, the bottom of the tab contains the level navigation
tools that allow you to view the different levels of the automaton.
The Level box simply displays the current level that is being viewed. The first four buttons move the viewing
level either forward or backward by either one level or 10 levels. The next button moves the viewing level back to the first level
and the last button allows you to input the level number to view. Note that this number must be in the range of
levels generated.
The Probability Density Viewer
The layout of the probability density viewer is similar to the level
viewer except that there are two lists to the right. The color scheme now
corresponds to subintervals of [0, 1]. The first color corresponds to
probability 0 and all other intervals represent of the form (a, b]. The
list to the left of the color scheme is a list of the group elements.
The way this mode works is you select a subset of elements from the
element list and refresh the image. For each cell in the automaton the program will
calculate the probability that an element from this subset is in that cell, using
level 0 to the current level.
When you move the mouse over the automaton the position you are pointing
at and the value the probability of that cell are displayed in the status
bar and if you hover for a few seconds over the automaton the position and
probability are also displayed as a tool tip close to the cursor.
If you double-click on a cell in the image or on a probability range
in the list a color chooser dialog box will appear allowing you to select
a new color for that range. Remember that you will need to select the
refresh button to see the color change.
If you right-click on the image or on a probability range
in the list a popup
menu will appear with the options to change the element's color, to make the
element transparent and to copy and paste a color. If you select to change
the element's color the same
color chooser dialog box will come up. If you select the transparent color
option then the displayed color in the selected probability range will be
an x, signifying a transparent color.
When the graph is refreshed the background color will show through the transparent
cells. Copy and paste will simply copy and paste the color to and from the
system clipboard.
The Level box works the same way as with the level viewer. In this mode
the image displayed will be the probability density from level 0 to the
current level.
The Image Menu Options
The File Options
- The Load Color Scheme option will load a previously saved color scheme into the list of current
color schemes the user can choose from. If the loaded color scheme has fewer entries then the current number of
elements the scheme will be cycled and if the loaded scheme has more entries than the current
number of elements the scheme will be truncated. Also if the name of the saved color scheme is the
same as the name of any currently loaded color schemes you will be prompted to select a different name.
- The Save Color Scheme option will save the color scheme to a file.
- The Save Image option will save the current image to either a bitmap, jpeg or png file.
- The Save Color Correspondence option will save the color/element correspondence to either
a bitmap, jpeg or png file. There are two sub-options for this menu item, one is to save the correspondence as
a single image and the other is to save it as multiple images. If you choose a single image the program will create
an image of the color/element data that has 25 elements per column and as many columns as it takes to fit all
of the elements. If you choose multiple images the program will save a sequence of image files with 25 elements
per file.
- The Save Data option has a submenu consisting of Current Level and Levels each of these has a submenu allowing
you to select between saving the data as a text file and a LaTeX file. Saving the current will simply save the data in
the level you are currently viewing. The levels option will allow you to select a range of levels for saving.
- The copy image, color correspondence, and data are the same as their saving counterparts except
that the information is copied to the clipboard. Also, as for the color correspondence, when copied to the
clipboard it is copied as a single image.
- The Save Level Animation Images option will render each level (time-step)
of the automaton as a set of image files that can be made into an animation
using an external animator. When you select this option a dialog box
will appear allowing you to input a base name of the images and the
type of graphics you want to save the images to (jpg, png or bmp).
The image filenames will be the base image followed by an underscore and
then followed by the level number.
- The Export to POV-Ray option will save the automaton as a set of files that can be read and rendered by POV-Ray.
POV-Ray is a freeware ray tracer which is available on all major platforms. In Windows, there is a very nice and easy to use
user interface. Most Linux implementations have a command line version that is included in the distribution.
For details on the options of the POV-Ray exporter see the POV-Ray Exporter page.
- The export to SVG file saves the image as a Scalable Vector Graphics file that can be read
by most web browsers and any SVG editing package.
The View Options
- The first two options toggle the viewing mode between the level viewer and the
probability density viewer.
- The Show Grid and Show Border options simply draw a grid or border on
the automaton level.
The Zoom Options
- The turn off zoom option sets the mouse actions back to their normal state. Zooming is done
through mouse actions on the image and hence when a zoom mode is on the mouse has more
functionality than usual. There are times when it is convenient to turn this mode off.
- The undo and redo options will undo and redo zooms. The program will hold a maximum sequence of
50 zooms.
- The zoom box option is one of the three zoom modes. When selected the cursor will change and when you
click and drag over the image a shaded box will be drawn. When you release the mouse the program will zoom
to the box you selected. Due to having to keep the aspect ratio the same you may get more than what you selected
but you will not get any less. To cancel a zoom, click the right mouse button while the left mouse button is
still down.
- The zoom in and zoom out options work the same way. When in either of these modes you simply click
on the image and the program will zoom the current zoom factor place the position of the click in the center
of the zoomed window. The current zoom factor can be set in the zoom factor option.
- The recenter option will simply recenter the image at the position of the click.
- The reset zoom to full view option will zoom out so that you can see the entire automaton image.
The Colors Options
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The menu on the left is the one for the level viewing mode and the on on the
right is for the probability density viewing mode.
- The reset to default color scheme option will reset the current color scheme to the
default colors. This scheme consists of a cycle of 60 distinct colors that begin with the
standard VGA 16 and then continue with combinations of these 16 to form a scheme
similar to the SVGA 64 sequence of colors. Most of the options in this menu will change
the color scheme and moreover link colors together so that changing one color changes the color
of all those elements that are linked to it. This option will not only reset the colors to their
original state but it will also break all of the color links, in essence, wiping the slate clean.
- The undo and redo options will undo and redo color scheme changes. The program will
hold a maximum sequence of 20 scheme changes.
- The Load Color Scheme option will load a previously saved color scheme into the list of current
color schemes the user can choose from. If the loaded color scheme has fewer entries then the current number of
elements the scheme will be cycled and if the loaded scheme has more entries than the current
number of elements the scheme will be truncated. Also if the name of the saved color scheme is the
same as the name of any currently loaded color schemes you will be prompted to select a different name.
- The Save Color Scheme option will save the color scheme to a file.
- The highlight elements option will color all of the currently selected elements in the element
list one color and all of the other elements another color. Furthermore, these sets of colors are now
linked together. So if you change the color of an element with the color chooser all of the elements
in that group are also changed to the new color.
- The highlight subgroup option will take all of the selected elements in the element list,
derive the subgroup generated by these elements, color all of the subgroup elements one color and
all the other elements another color. As with the highlighting elements option the elements are
linked as well.
- The group elements option will take the currently selected elements, link (or group) them
and color them all the same color. The difference between this and the highlight elements option
is that the unselected elements are unaltered.
- The group subgroup option will take the currently selected elements, derive the subgroup
generated by these elements, color all of the subgroup elements one color and link them.
The difference between this and the highlight subgroup option
is that the elements that are not in the subgroup are unaltered.
- The group left cosets and right cosets option will take the currently selected elements, derive
the subgroup generated by these elements, color all of the subgroup elements one color and link
them. It will then find each coset link and color them.
- The set background color option will invoke a color chooser dialog box to allow the user
to select a different background color.
- The new color scheme option will load a new (default) color scheme into the list of available
color schemes.
- The rename color scheme option will bring up a dialog box that will allow you to select a new
name for the color scheme.
- The number of probability intervals lets the user select the number
of different colors to use in the probability density viewing mode. The
interval [0, 1] is divided evenly into this number of subintervals. A cell
is then colored by the interval color where the cell probability lies.
- The refresh color scheme will simply refresh the color/element list, it will not refresh the image.
That is the job of the refresh button in the upper right. Theoretically you should never need to
use this option since the color correspondence is updated after each change to the color scheme.
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