Graphs and diagrams:

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

"Step-by-step iteration >"

Selects a graph that allows you to monitor each iteration step.

"Step-by-step inverse iteration >"

Selects a graph that allows you to monitor each iteration step, but now it takes the 'inverse' of the selected function (i.e. 'z -> sqrt(z - c)' instead of 'z -> z² + c' ).

"Orbit diagram for variable z (Julia) >"

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

"Orbit diagram for variable c (Mandelbrot) >"

Same as the previous one, except that it plots the orbit for each 'c', where 'z' remains constant.

Each of the graphs has a sub menu, for "Step-by-step iteration >" and "Step-by-step inverse iteration >" the menu contains the following options (shapes):

"Point >"

Use a point as starting value.

"Line >"

Use a line as starting shape.

"Circle >"

Use a circle as starting shape.

"Rectangle >"

Use a rectangle as starting shape.

Each of the shapes has a sub menu which allows you to select the type of coloring. Note: the colors will wrap the maximum number of colors - 1. You can choose from three different options:

"Color depends on starting point"

Each iteration has it's own color.

"Color depends on iter. steps"

Each iteration step has it's own color.

"All iteration steps same color"

All steps and iterations in one color (default is 'purple').

The two orbit diagrams, "Orbit diagram for variable z (Julia) >" and "Orbit diagram for variable c (Mandelbrot) >" , have a sub menu to select a diagram:

"Filled-in"

Plots only the points inside the set.

"Escape time diagram"

Plots both, points inside and outside the set. Points outside the set get a color that represents how many iterations were required before |z|>2. This is the well-known set-with-colored-bands diagram.

"Boundary trace"

This traces the boundary of the set.

"Inverse iteration method"

Uses the inverse function to draw "Orbit diagram for variable z (Julia)". The option is only available for this graph.

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

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

Functions:

Available functions:

• z -> z ^ 2 + c
• z -> z ^ 3 + c
• z -> z ^ 4 + c
• User defined

The user defined function requires some explanation:

• Only the part which follows 'z ->' can be entered.
• Variables (z,c) and function names are case insensitive.

Operators		Functions 1
+	add	sin	sine
-	subtract	cos	cosine
*	multiply
/	divide

Complex numbers are surrounded by '{' and '}' brackets. For example, you can write 'c * z * (1 - z)' as:

• c*z*({1,0}-z)
• c*z*(1-z)

The first value is the 'real part' and the second value is the 'imaginary part' of the complex number.

You can only omit the brackets if the 'imaginary part' is 0.

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:

"Real part of c:"

The real part of value for c.

Applies to: "Step-by-step iteration >" , "Step-by-step inverse iteration >" , "Orbit diagram for variable z".

"Imaginary part of c:"

The imaginary part of value for c.

Applies to: "Step-by-step iteration >" , "Step-by-step inverse iteration >" , "Orbit diagram for variable z".

"Real part of z:"

The real part of value for z.

Applies to: "Orbit diagram for variable c".

Imaginary part of z:

The imaginary part of value for z.

Applies to: "Orbit diagram for variable c".

"Min. for real part of values:"

The lowest x coordinate.

Applies to: all graphs.

"Max. for real part of values:"

The highest x coordinate.

Applies to: all graphs.

"Min. for imaginary part of values:"

The lowest y coordinate.

Applies to: all graphs.

"Max. for imaginary part of values:"

The highest y coordinate.

Applies to: all graphs.

"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 >". "Step-by-step inverse iteration >"

"Total number of iterations:"

The maximum number of iterations.

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

"Number of skipped iterations:"

The number of iterations which is not plotted.

Applies to: "Orbit diagram for variable z" , "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:

Point

When you enter this 'shape', the following help menu will appear:

ENTER	Start selection
Mouse position	Starting point
ESCAPE	To central menu

The position of the mouse is the begin point. As you move the mouse, you can see the value in the status bar at the bottom of the screen. Press the right mouse button to start a new selection.

As soon as you press <Enter>, a small filled circle will appear at the current position of the mouse-pointer. This is the starting value. This also marks the end of the selection process. When you press <F1> you will see the available keys:

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

<Enter> exits the help menu and resumes the iteration mode, you can move the mouse without disrupting the process. To start a new selection, click on the right mouse button.

At the bottom of the screen, in the status bar, you can see the current iteration step and value.

Line

When you enter this 'shape', the following help menu will appear (it also applies to "Rectangle" and "Circle").

ENTER	Start selection
L-button	First/second point
R-button	New selection
ESCAPE	To central menu

To draw a line, move the mouse to the position on the screen where you want to start the line and press the left mouse button. Move the mouse, while you hold down the left mouse button, to the point where you want the line to end, and release the button. You can monitor the position of the begin and end point in the status bar at the bottom of the screen. In case you want to restart the selection, you must press the right mouse button.

Rectangle

To draw a rectangle, move the mouse to the position on the screen where you want the upper left corner to be. Move the mouse, while you hold down the left mouse button, to the lower right corner of the rectangle, and release the button. You can monitor the coordinates in the status bar at the bottom of the screen. To restart the selection, press the right mouse-button.

Circle

To draw a circle, move the mouse to the position on the screen where you want the centre, and press the left mouse button. Move the mouse, while you hold down the left mouse button, to the point where you want the perimeter to be, and release the button. You can monitor the values for the centre and radius in the status bar at the bottom of the screen. Click on the right mouse-button to restart the selection.

Iteration

<Enter> starts the iteration, this also ends the selection of a shape. When you press <F1> you will see the available keys:

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

Step-by-step inverse iteration:

Since the previous paragraph, on "Step-by-step iteration", covered the selection of shapes, I will now focus on the iteration process (which is slightly different from the previous graph).

Point

When you press <F1> you will see the available keys:

+	Pos. root
-	Neg. root
ENTER	random root
DELETE , <d>	Erase screen
R-button	New selection
ESCAPE	To central menu

Line , Rectangle and Circle

When you press <F1> you will see the available keys:

=	both roots
+	Pos. root
-	Neg. root
ENTER	random root
DELETE , <d>	Erase screen
R-button	New selection
ESCAPE	To central menu

The status bar doesn't show iteration step and values for the three shapes (line, rectangle and circle).