| A Quick Guide to the Dynamical Grapher for Quadratic Maps |
| FEATURE |
DESCRIPTION |
| "+,-" Buttons | These are the parameter adjuster buttons. They increment the value of the parameters and re-draw the curves with the new values. |
| C1-C6 | Use these tabs to define parametric plane curves by entering values and/or mathematical expressions in the coefficient textfields. |
| Calculate |
Clicking this button under the
FC tab calculates a sequence for the probabilistic function
composition. The length of the composition sequence is determined by
the maximum iteration value entered for FC under the curve tabs. |
| Clear
Buttons |
These buttons reset the curve
and function tabs to their default settings. |
| Color
Selection Boxes |
Clicking a color box allows the
user to choose a different color for the corresponding graphing feature. |
| Curve
Tabs |
Use these tabs to define
parametric plane curves C1-C6 by entering values and/or mathematical
expressions in the coefficient textfields. |
| Discontinuous |
When this Options Menu feature
is active the grapher plots curves as sets of points as opposed to
polygonal paths. |
| F1-F4 |
Use these tabs to define
quadratic rational functions by entering values and/or mathematical
expressions in the coefficient textfields. |
| Fade |
This curve tab feature makes the
iterated images appear to fade as the iteration number goes up or down
depending on whether "Low" or "High" is selected. |
| FC
Checkbox under the FC Tab |
This checkbox is associated to
the graph trajectory feature. It stands for "Functions Colors." When
this checkbox is active the graph trajectory feature will draw using
the colors selected for functions F1-F4 depending on the function used
for the particular iteration. When this checkbox is not active the
graph trajectory feature will use the same color for each iteration no
matter which function is being used for the particular iteration. |
| FC
Tab |
Use this tab to define a
function that a composition of functions F1-F4. |
| Function
Checkboxes |
Activating these checkboxes
under the curve tabs instructs the grapher to draw the iterated images
of the curve under the corresponding function. |
| Graph
Trajectory |
Activating these checkboxes
under the function tabs instructs the grapher to draw the orbit of the
location of the mouse pointer when placed on the drawing window. |
| GraphCurves |
This button graphs the curves
under the current settings. |
| Iterations |
This curve tab feature allows
the user to enter a range for the iterated images of the curve under
repeated applications of the functions. |
| Iters= |
In these textfields, the user
may enter the number of points graphed in an orbit under the graph
trajectory feature. |
| Min/Max |
The user may use these
textfields under the curve tabs to enter the minimum and maximum
iterate for the grapher to display. |
| None/Low/High |
These are the possible settings
for the "Fade" feature under the curve tabs. If "Low" is selected the
lower iterations will display as more faded. If "High" is selected, the
higher iterations will display more faded. |
| Parameter
Checkboxes |
Marking the check boxes on the
left of parameters "a,b,c,…,l" links those marked parameters so that
they increment together when a corresponding "+,-" button is pressed. |
| Parameter
Increment Values |
The textfields between the
parameter values and the "+,-" buttons contain the values that the
"+,-" buttons will increment or decrement the parameter by. |
| Parameter
Values |
The textfield on the right of parameters "a,b,c,…,l" shows the current parameter values. |
| Parameters
"a,b,c,…,l" |
These letters may be used to
define the coefficients for functions F1-F4 and curves C1-C6. The
parameter value textfields and "+,-" buttons allows the user to adjust
these parameters. |
| Parser |
Use this textfield to write
equations defining relations between parameters used in the curves and
functions. Each equation should end in a semi-colon. All usual math
operations (+,-,*,/,^) should work here. For example, if the user uses
parameters m1 and m2 when defining coefficients for functions and/or
curves they could enter "m2=-3*m1^2-1;m1=a;" into the parser to define
m2 interms of m1 and allow for control of m1 via the paramter "a". |
| Print
Funcs/Curve |
This Actions Menu feature saves
the current functions and curves to a .txt file. |
| Probabilistic |
Selecting this option under the
FC tab allows the user to enter frequencies for each of the functions
F1-F4 to define the function FC probabilistically. For example,
P(F1)=1, P(F2)=1, P(F3)=2, and P(F4)=0 would mean that on average FC
would take the values F1 and F2 one out of 4 times, the value F3 half
of the time, and never take the value F4. |
| Probability
Textfields (P(Fi)) |
These are for entering
frequencies for each of the functions F1-F4 to define the probabilistic
function composition FC. For example, P(F1)=1, P(F2)=1, P(F3)=2, and
P(F4)=0 would mean that on average FC would take the values F1 and F2
one out of 4 times, the value F3 half of the time, and never take the
value F4. |
| R/F/P
Buttons |
Instead of the user trying to
use the mouse to point to an exact spot, the user may simply type in
the coordinates into the "x cur" and "y cur" textfields and press the
"P" ("Play") button to automatically view the trajectory from the given
point. The "F" ("Freeze") button freezes the trajectory that has been
created on the drawing window. Finally, the "R" ("Record") is a toggle.
When the user presses "R" any trajectories that the user has frozen
will be recorded to a text file one the user "turns off" the R button. |
| Save/Load
State |
This File Menu feature saves and
loads settings files (.waa files). |
| Set
1/Set 2 |
This is the set of parameter
adjusters. |
| Show
Trajectory Points |
When this Options Menu feature
is active the Graph Trajectory feature enlarges the points in the
orbit, making them easier to see. |
| Showcurve |
When this feature is active the
grapher will draw the corresponding curve (C1-C6) when the GraphCurves
button is clicked. |
| Take
Screen Shot |
This Actions Menu feature saves
the drawing window as a .png file. |
| tmin/tmax |
The values determining the range
of the parameter "t" used to define a parametric curve. |
| U/D/L/R |
The up/down/left/right buttons
shift the view of the drawing window. |
| Use
Function Colors |
The user may select this option
under the FC tab when the probabilistic function composition is chosen.
When this option is active the grapher will use the colors chosen for
F1-F4 for FC depending on which of F1-F4 is being used for each
iteration. |
| User
Defined |
When this option is selected
under the FC tab the user can enter a sequence from the set {f,g,h,i}
into the textfield to define the function composition FC. For example,
entering "fgfh" would define FC as F1(F2(F1(F3))). |
| x
cur/y cur |
This shows the location of the
mouse pointer on the drawing window. |
| x
min/x max/ y min/y max |
These values determine the view
for the drawing window. |