One first must load a previously saved session or enter in a collection functions manually together with the session parameters (POINTS TO PLOT, SKIPS, and SEED VALUE). The INPUT FUNCTIONS and SESSION PARAMETERS will appear in the left window.  Note that you can edit, delete, or clone an existing INPUT FUNCTION by right clicking on it.  In order to see pictures of the desired sets one needs to:

1. select some or all of the functions (Ctrl+click or Shift+click can be used to select multiple functions) and
2. set the SET TYPE to either ATTRACTOR or JULIA and
3. set the PROCESS TYPE to either FULL or RANDOM and
4. click the button for COMPOSITE, INDIVIDUAL, OR COMPOSITE AND INDIVIDUAL.

The COMPOSITE button will create an OUTPUT SET by using all of the selected INPUT FUNCTIONS "in parallel".  This is sometimes called the OUTPUT SET of the semigroup generated by the selected INPUT FUNCTIONS.  The INDIVIDUAL button will create multiple OUTPUT SETS, one for each of the selected functions.  If only one INPUT FUNCTION is selected, the COMPOSITE button and the INDIVIDUAL button will do the same thing.  The COMPOSITE AND INDIVIDUAL button creates the same OUTPUT SETS which would be created by hitting both the COMPOSITE button and INDIVIDUAL button separately.  For more details see Julia sets for rational semigroups and Attractor sets for an Iterated Function System (IFS),

The OUTPUT SETS images are displayed in the middle window and are listed in the right window.  The user can then toggle on/off the sets to be viewed (Ctrl+click or Shift+click can be used to select multiple OUTPUT SETS to be viewed together).  See VIEWING OPTIONS AND CONTROLS for more info on how to change color, delete, view properties, zoom, shift, turn on/off grid and axes, adjust dot size, create/remove multiple OUTPUT GRAPH tabs, reset zoom, re-center, and open an overview window. 

The user can produce a new OUTPUT SET created by taking the INVERSE IMAGE of a selected OUTPUT SET (or union of multiple selected OUTPUT SETS) under a selected INPUT FUNCTION by clicking on the INVERSE IMAGE (RANDOM/FULL) button. 

• If the FULL button is selected when the INVERSE IMAGE (RANDOM/FULL) button is pressed, the full inverse image of the selected OUTPUT SET (or union of multiple selected OUTPUT SETS) will be created.  This means that ALL pre-images (under the selected INPUT FUNCTION) of the points in the selected OUTPUT SET (or union of multiple selected OUTPUT SETS) will be used to comprise the new OUTPUT SET. 
   
• If the RANDOM button is selected when the INVERSE IMAGE (RANDOM/FULL) button is pressed, a partial inverse image (under the selected INPUT FUNCTION) of the selected OUTPUT SET (or union of multiple selected OUTPUT SETS) will be created. Specifically, for each of the points in the selected OUTPUT SET (or union of multiple selected OUTPUT SETS) only one randomly chosen pre-image will be included the new OUTPUT SET. 

Note:  If multiple INPUT FUNCTIONS are selected, the INVERSE IMAGE (RANDOM/FULL) button will create a new OUTPUT SET for each INPUT FUNCTION. 

Note:  If the JULIA cannot compute all inverse images of a point under the selected INPUT FUNCTION (e.g., when the INPUT FUNCTION is Real Affine Linear with determinant 0), then JULIA will return a warning message that such an action is not allowed.

The user can produce a new OUTPUT SET created by taking the FORWARD IMAGE of a selected OUTPUT SET (or union of multiple selected OUTPUT SETS) under a selected map by clicking on the FORWARD IMAGE button.  Unlike the INVERSE IMAGES (RANDOM/FULL) button, the FORWARD IMAGE button will produce the same OUTPUT SET no matter which PROCESS TYPE (FULL or RANDOM) is selected. 

Note:  If multiple INPUT FUNCTIONS are selected, the FORWARD IMAGE button will create a new OUTPUT SET for each INPUT FUNCTION. 

Images may be saved as either .jpg or .gif files.  You can do this by clicking on the SAVE IMAGE icon at the top of the window (or by going to FILE -> SAVE IMAGE).  When typing in the file name that you wish to save the image under, you must include the file extension (e.g., imagename.jpg or imagename.gif). 

Images may be printed by clicking on the PRINT IMAGE icon at the top of the window (or by going to FILE -> PRINT IMAGE).

A SESSION may be saved by clicking on the SAVE SESSION icon at the top of the window (or by going to FILE -> SAVE SESSION).  This will save your session in a .julia.zip file which itself contains multiple files.  One such file will be called session.txt and it will save the SEED,  MIN POINTS TO PLOT,  SKIPS values and the current state of the SET TYPE (JULIA OR ATTRACTOR)  and PROCESS TYPE (RANDOM OR FULL).  Each INPUT FUNCTION will have be saved in a text file of the form in.********.txt  where ***** is a number which is assigned by Julia to uniquely identify this function (it is connected to the time the file was created).  Each OUTPUT SET is saved in two files of the form  out.********.txt and out.********.dat, where again ***** is a number which is assigned by Julia to uniquely identify this set.  The .dat file contains the ordered pairs (in a format compatible with Mathematica) and the .txt file contains the HISTORY information (which shows how the selected OUTPUT SET was created, including information on the creation of any auxiliary OUTPUT SETS which were needed). 

Note that the session files created by Julia can be modified outside of Julia (without using Julia) in order to do such things as add INPUT FUNCTIONS from one SESSION into another SESSION, add OUTPUT SETS from one SESSION into another SESSION, and add OUTPUT SETS created by other applications (such as Mathematica) to a SESSION.  To learn how to modify a SESSION go here.  The new SESSION can then be loaded into Julia (see below).

A previously saved SESSION may be loaded by clicking on the LOAD A NEW SESSION icon at the top of the window (or by going to FILE -> LOAD SESSION).  You will then be asked to select a session file from your system.  The current version Julia 2.0 will load the new .julia.zip files as well as the old Julia 1.0 files (.julia), but, if you load and then resave such a SESSION a new .julia.zip file will be created in the new format. 

You may view and/or download  EXAMPLE SESSION files here.