Gasket's Features

This document describes the basic functions of Gasket, on or about 14 January, 1996. If this document hasn't been updated in a while, (reload, just to be sure), the program may have evolved beyond the state it was in when this was last updated. To get the real story, harrass msouth@shodor.org about it.

The following assumes that you are familiar with the document "How Gasket Works".

Basic Operation

Gasket operates with a simple (read "primitive") interface. The user sees an HTML form with an image (either a number of points or line segments or both, along with several multi-colored, rectangular "control points") and a smattering of radio buttons, popup menus, checkboxes and submit buttons. The desired options are selected using these mechanisms of choice, and the form is "submitted" by either clicking on the image or a sumit button. At this point, the user's desires are communicated to a remote server, and a page is returned with a newly-drawn image which reflects the options and/or actions selected by the user.

At the most basic level, the user clicks on the picture to indicate either a "seed point" or a desired location for a control point, and an image is returned showing the result of this action. (The method the computer uses to draw the image is described in "How Gasket Works".)

Settings and Options

Plot [number of points]: The popup menu indicates how many points to plot each time. Set to zero if you want no points plotted.
Color Code: When this box is checked, the points plotted (and the traces, if any) will be colored according to the control point that was selected by the drawing algorithm. For example, if the computer chooses to move toward the green point, it will color the point it plots there green..
Show Traces: Rather than simply moving from one point to the next, a line is plotted between successive points.
Big Dots: This makes the points plotted slightly larger in order to make them more easily seen. If this option isn't checked, the points are the size of a single pixel.
Randomize: When this is checked, Gasket uses a different sequence of random numbers each time. This is usually what you want. However, at times you may want the computer to use the same sequence of random numbers on successive runs. In that case, uncheck this box and the same sequence will be used until the box is checked again (what that means is that the computer will choose which control point to move toward in exactly the same order each time).
Add to current picture (checkbox): When checked, the results of the next action will be plotted on top of the current picture. For example, if the current picture shows 10,000 color-coded points, and you select a non-color-coded, traced plot of ten points, those traces will show up on top of the 10,000 color-coded points. This is useful when you want to see the effect of slowly adding more and more points to the picture, or to illustrate the algorithm the computer is using to draw the points.
(A really cool thing you can do here is show that, for a given sequence of random numbers, you eventually end up going to the same locations (at least to within pixel resolution) no matter where you choose the initial point. You can see this by setting the number of point to plot to ten, turning on "show traces" and perhaps "color code", and turning off "randomize". Now click anywhere on the image. Make sure "add to current picture" is checked, and click anywhere else (a centimeter or so awya from the first click is a good option). On the resulting figure, you will be able to see that the two paths get closer together at every step. In the infinite limit, the paths get inifinitely close together. Click on a few other locations around the picture to add to the effect.)
Draw Lines: When this box is checked, Gasket will draw lines on the picture according to a non-random algorithm that, in many cases, gives a very good idea of what the long-range behavior of the point-plotting process will look like.
The rules for the line drawings work as follows. At the zeroth level, lines are drawn connecting each control point to the next one in the order they appear in the "Move Point" selection menu. Iteration one is drawn by taking each of these line segments and moving every point on the segment toward each control point according to the movement ratio specified for that control point. This is accomplished by moving the endpoints of each segment according to the ratio and then reconnecting them at their new location.
The second iteration moves each of the lines from the first iteration toward each control point and replots them. The third iteration similarly operates on the lines plotted by the second iteration, and so on.
Draw All Iterations: When this is checked, all of the iterations up to the selected number are drawn. When unchecked, only the indicated iteration is drawn.
Move [color] point: When this box is checked, the indicated control point will move to the location that the user clicks.
Reset | Change Number of Points: This button has two basic functions. First, it is a simple way to quickly move all the control points back to their original positions. Second, it can be used to change the number of control points to the number indicated in the popup menu right below it.
In addition to moving the points to their default positions it will reset the movement ratios and the relative probabilities to their default values. (Note: To change the number of control points, you must click the Reset | Change Number of Points button. Simply changing the popup menu and then clicking on the image will not affect the number of points.)
Movement Ratios: These ratios are those used by the drawing algorithms to determine how far to move toward a given point. For example, if the ratio for the green point is .4, then whenever the green point is selected, the machine moves four tenths of the way toward the green point and plots a point.
To set all of these ratios to the same number, check the "Set All To:" box and enter the ratio in the text window.
Relative Probabilities: These numbers indicate the relative probability that a given control point will be chosen on any step in the random drawing process. The actual probability can be computed by totaling the relative probabilities and then dividing each relative probability by this total. Setting them all to the same thing (which will make all probabilities equal) is accomplished by checking the "Set all to:" box and typing a number into the text window.
Dehanced for Internet Explorer and Mosaic: This is automatically "checked" (that is, the checkbox is ignored, and treated as if it's checked no matter what the user does) if you are using Internet Explorer or Mosaic. These browsers do not send the correct coordinates when the submit image is in a table. If you find that the points you are clicking seem to not match the output, you may want to try checking this box and seeing if that fixes things. if it does, please email msouth@shodor.org and tell me what kind of browser you are using.