Graphs and diagrams:

For "Functiontype: From R to R", the following graphs are available:

"Step-by-step iteration >"

Selects a graph that allows you to monitor each iterationstep.

"Orbit diagram for variable x"

Selects the graph that plots the orbit for each 'x'. The 'c' remains constant.

"Orbit diagram for variable c"

Same as the previous one, except that in this case the orbit is plotted for each 'c', where 'x' remains constant.

"Step-by-step iteration >" allows you to select a diagram:

"Webdiagram"

Draws the function graph and the line for which x is equal to y. Each time you press <Enter>, a vertical line is drawn to the x=y line and a horizontal line back to the function graph.

"Iteration values"

You can select a 'c' with the mouse, small horizontal lines are drawn at the current iteration value.

"Stepdiagram"

Same as "Iteration values" but with the difference that each horizontal line shifts a bit to the right.

"Combination of webdiagram and stepdiagram"

For this combination of diagrams, the screen is divided into four sections. Each diagram uses one quarter of the screen, the rest remains unused (this is to avoid problems with the aspect ratio). The lower left part of the screen is reserved for the "Webdiagram", and the lower right part of the screen is reserved for "Stepdiagram".

With <Escape> you can abort the calculation (Orbit diagrams).

You can activate the central menu with <Escape> (All graphs).

Functions:

There are six predefined functions. The last one is open, and you can select it to enter your own function.

• x -> x² + c
• x -> frac(cx)
• x -> c * cos(x)
• x -> cx(1 - x)
• x -> -cx³ + (c + 1) x²
• x -> c(1 - |2x - 1|)
• User defined

The user defined function requires some explanation:

• Only the part which follows 'x ->' can be entered.
• Variables (x,c) and function names are case insensitive.
• For sin(), cos() and tan() arguments are in radians.

Operators		Functions 1		Functions 2		Functions 3
+	add	sin	sine	exp	exponent	abs	absolute value
-	subtract	cos	cosine	log	natural logarithm	entier	entier 1)
*	multiply	tan	tangent	sqr	squareroot	frac	fraction 2)
/	divide	asn	arcsine
^	raise to power	atn	arctangent

1) entier(x) = [x] := the largest integer value less or equal to x

2) frac(x) := x - [x]

Parameters:

The parameter menu requires some explanation.

The line at the bottom of the screen lists the available keys, they apply to edit-fields and menu's in general. The keys at the top of the screen are specific to the parameter-menu.

The following list explains each of the items in more detail:

"Value for parameter c:"

The value for c.

Applies to: "Step-by-step iteration" , "Orbit diagram for variable x".

"1st starting value for iteration:"

The initial value for x, you want to start with. When you change this value, the value for the other starting value will change as well.

Applies to: "Step-by-step iteration" , "Orbit diagram for variable c".

"2nd starting value for iteration:"

Same as the previous one. If you change this, the previous startingvalue remains unaffected. Both iterations will be presented in different colors.

Applies to: "Step-by-step iteration".

"Estimated lowest value:"

This is the estimated lowest value for x and y.

Applies to: "Step-by-step iteration".

"Lowest value for x"

This is the lowest value for x.

Applies to: "Orbit diagram for variable c".

"Lowest value for c"

This is the lowest value for c.

Applies to: "Orbit diagram for variable x".

"Estimated highest value:"

This is the estimated highest value for x and y.

"Highest value for x"

This is the highest value for x.

Applies to: "Orbit diagram for variable c".

"Highest value for c"

This is the highest value for c.

Applies to: "Orbit diagram for variable x".

"Escape value:"

Escape value, sometimes called "Bailout value". Under normal circumstances this value is calculated automatically. As soon as you change the value, a (red) asterisks will appear, indicating that it is your responsibility now.

Applies to: all graphs.

"Number of steps/iteration:"

This is a bit misleading, because it is the number of times the function is iterated each time you press <Enter>.

Applies to: "Step-by-step iteration".

"Total number of iterations:"

The maximum number of iterations.

Applies to: "Orbit diagram for variable x" , "Orbit diagram for variable c".

"Function N times iterated:"

The n-th iterated of a function. When drawing the function, the function is N times iterated.

Applies to: "Step-by-step iteration".

"Number of skipped iterations:"

The number of iterations which is not plotted.

Applies to: "Orbit diagram for variable x" , "Orbit diagram for variable c".

The following keys apply to the parameter menu:

<F3>:	Back to default coordinates for this diagram
<F5>:	Reset "escape value" to it's original (automatically) calculated value.
<Cursor Up>:	Move one item up
<Cursor Down>:	Move one item down
<Cursor Left>:	Move the cursor one character to the left
<Cursor Right>:	Move the cursor one character to the right
<Esc>:	To previous menu
<Delete>:	Delete the character under the cursor
<Backspace>:	Delete the character left from the cursor

With <Esc> you can exit this menu and go back to the main menu.

Step-by-step iteration:

When you enter this graph, the help menu will appear:

ENTER	Iterate
DELETE , <d>	Erase screen
R-button	New selection
ESCAPE	To central menu

Press <Enter> to exit the help menu. You can always press <F1> to access the help menu again.

Webdiagram:

Default, the 1st and 2nd starting value you entered in the parameter menu are used. Press <Enter> to start iterating, the first time you will only see a spot (pixel) on the x=y line at the 1st and/or 2nd starting value position(s). The second time you will see the result after the first iteration. Each time you press <Enter>, the selected function is iterated, and the values after 'n = ' (the current iteration step) and 'x = ' (the current iteration value) change (see the status bar at the bottom of the screen).

When you press the right mouse button, a mode is selected that allows you to specify a starting value by moving the mouse pointer. The pointer is locked to the x=y line to make it easier to select a value. The mode is active until you exit the diagram.

Each iteration has it's own color, though the colors will wrap at the iteration-number that is equal to the maximum number of colors - 1. In the mouse mode you can always press <Delete> or <d> (erase screen) to use another color for the current iteration (as long as you don't move the mouse, the starting value is preserved).

Iteration values:

This diagram works pretty much the same as the previous one. The major difference is the way the values are presented. Selecting a new starting value with the mouse is different too: you have to move the mouse horizontally to select one.

Stepdiagram:

This diagram works the same as the previous one, except of course for the way values are presented.

Combination of webdiagram & stepdiagram:

In this diagram, the lower left quarter of the screen and the lower right quarter of the screen are used. At the left you will see the "webdiagram", and to the right the "stepdiagram". You can use the mouse on the x=y line to select a new starting value.