PascGalois Zn Help: 1-D Cellular Automata Image Screen
The Image Screen
The image screen is where you will be doing most of your explorations.
The screen 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.
The layout of the screen 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.
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.
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.
The Image Menu Options
The File Options
- The load color scheme options 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 counts item will save element counts to either a text file or as a LaTeX table. See the section on counts
below.
- The save selected data option will save the data elements in the current selected region to either a
text file or a LaTeX array. See the section on counts below for a more detailed description of the process for
selecting regions.
- The copy image, color correspondence, counts 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 color animation image sequence option will create a sequence of images (bitmap, jpeg or png) that
go from one color scheme to another. To use this option you need to have at least two color schemes loaded.
When you select this option you will get the following dialog.
Select the beginning and ending color schemes by using the drop-down boxes at the top. Select a base
filename by selecting the browse button and typing in the directory and name you want. The actual filenames will
be the base name followed by an underscore and then a four digit number, in sequence, of course. Select the file
type and the number of frames (that is, files) you want in the sequence and click OK. The program will then create a
sequence of image files that smoothly go from the beginning color scheme to the ending color scheme. You can then
use a different program to create a video file out of this set of images.
- 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 Options Options
- The input number of rows allows you to select the number of rows that will be graphed. The number you
specify will be the number of rows graphed after the seed. So if you have one seed row and select to graph 100 rows
there will be 101 rows of the automata visible.
- The use column alignment option is a toggle between column and pin alignment.
If you are creating an infinite automaton you can set the
way the data is arranged. The pin alignment will arrange the data in a manner
similar to the way we usually write Pascal's Triangle. For example,
The same data aligned in a column alignment would look like,
If you are graphing a finite automaton the alignment will be a column alignment and this option
will not appear on the menu.
- The draw squares is a toggle between drawing circles and squares.
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. This option
will also turn off any selection mode, discussed later.
- 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
- 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 options 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 / ideal option will take all of the selected elements in the element list,
derive the subgroup (or ideal) generated by these elements, color all of the subgroup (ideal) 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 / ideal option will take the currently selected elements, derive the subgroup (ideal)
generated by these elements, color all of the subgroup (ideal) elements one color and link them.
The difference between this and the highlight subgroup / ideal option
is that the elements that are not in the subgroup are unaltered.
- The group 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 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.
The Counts & Data Options
- The turn off region selector option sets the mouse actions back to their normal state. Selecting
regions for counts or data extraction is done
through mouse actions on the image and hence when a selection mode is on the mouse has more
functionality than usual. There are times when it is convenient to turn this mode off. This option
will also turn off any zoom mode.
- The undo and redo options will undo and redo selection changes. The program will
hold a maximum sequence of 100 selection changes.
- The select region option will turn on the region selection mode. Each region that can be selected
is a triangle. To select a region click on a cell entry in the image, move to the second vertex of the
desired triangle and click again, finally move to the last vertex and click again. The region will
then be highlighted. Multiple regions may be selected at one time. To select a line simply
click twice on one endpoint. To select a point click that point three times. When selecting a
point two or three times do not click the mouse too fast or the computer will see that as a
double-click and think you wish to change the element's color.
- The unselect region option works the same way as the select region except that it unselects
the cells in the region.
- Select all and select none options simply selects the entire automaton or unselects the entire
automaton.
- The select and unselect rows option allows the user to select or unselect a range of
rows. When this option is selected you will see a select (or unselect) rows dialog box
Simply input the starting and ending rows and click OK.
The rows will then be highlighted. Remember that the row numbering starts at 0.
- The select and unselect region using positions allows the user to input the positions
of the triangle vertices in a dialog box, instead of by clicking on the image. When selected
the following dialog box will appear. Simply put in the row and column positions of the
vertices and click OK. Remember that both the row and column numbering start at 0.
- The set selection border color brings up the color chooser dialog box that allows
the user to select the color of the border used in the highlighting scheme for selected
cells.
- The set selection crosshatch color brings up the color chooser dialog box that allows
the user to select the color of the crosshatch used in the highlighting scheme for selected
cells.
- The display counts option will count the elements in the selected region as well as count the
elements in the entire automaton. These counts are then displayed in the following
dialog box.
In the counts display to the left there is a list of all the elements in the
automaton and the counts of the those elements in the selected region and in the total
automaton. The small toolbar at the top has options for saving and copying the
table of counts as text or LaTeX.
On the right is another element list that can aid in the counting of subsets
and subgroups. If you make a selection in this list the total of the selected and total counts
is displayed at the bottom. The small toolbar at the top has three simple options. The first selects
all of the elements in the list, the second unselects all of the elements in the list and the
third selects the subgroup generated by the currently selected elements.
- If you are exploring a finite automaton you will see another option below the display
counts, display period. When you select this option the program will determine the
period of the automaton, or tell you that it could not find it. If one is found, a message box
will appear with the period as well as a range of rows that contain a single period.
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