Manual for the Pentagon program.
This program makes a series of lines and tries to find regular pentagons with in-scribed stars. From a starting point lines are drawn perpendicular to a normal of 0º. The distances between these lines are either "Big" (= "B" = φ+2) or "Small" (="S" = 2φ-1). The starting point is given in an integer plus an integer times φ. So start position c = n +m φ, with n and m an integer. This system is repeated for angles of 72º, 144º, ect. Using this construction many pentagons with in-scribed stars can be found if m/n ≈ φ. For every value of n there will be 4 to 5 successive values for m that will given pentagons in the figure. So by far most values for m will not yield any pentagon at all. This program calculates in a kind of Golden Section numbers, defined as:
Z = Un + Gs*φ. With Un, and Gs integers.

Starting the program.
The series that determines the big and small distances (the B's and S's) is generated by an internal algorithm. The start point of the series is calculated by a ratio, in a way that makes sure the center of the figure is more or less in the center of the pattern of lines. After the figure is drawn, some focus rectangles are drawn over it. These indicate the center and magnification. With the arrow keys and <Page Up> and <Page Down> you can change the center and magnification. With the use of <Ctrl> the action will be ten times stronger. You can also set the new center with a mouse click. Give <Enter> and you will get a menu with parameters, and with a second <Enter> (or by clicking <OK>) the figure will be drawn with the new parameters. 
You can also enter the new center of the figure with a mouse click. Double clicking will redraw the figure. The internally generated series gives a rather big figure: about 3000 lines.

Changing the offset of the series of lines.
If you press <Tab>, you will see the focus rectangles disappear, and the arrow keys don't change the position of the figure but the offset of the series of lines. The values of the offset is displayed in Un = Units, and Gs = times φ on the bottom of the window. You will notice that the ratio Gs/Un needs to be more or less equal to φ, otherwise no pentagons will be found. <Page Up> will make Un = Gs/φ, and <Page Down> makes Gs = Un*φ. The figure will be redrawn after each key press. For each value of Un there will be 4 to 5 subsequent values of Gs that will yield pentagons in the figure. You can change the reference position by right clicking on the vertical line that you want to be the new reference line. By doing this you will see the offset has been changed. This is to make sure the new reference point and new offset make the same figure.

Changing parameters.
Pressing <Enter> will give a dialogue menu with the parameters of the figure. Most parameters are straightforward: the size of the picture, the center, the magnification, and with item are to be drawn, and the offset of the lines expressed in Un and Gs. The same dialogue menu can be obtained via the menu bar under the item "File". The colors of the items and lines can be changed via menu item "Colors". The figure can be stored as a Bitmap (=BMP file).

Storing and reading parameters.
You can store the parameters in a readable format. Most items in the file are obvious. The series of B's and S's start on lines 3 and ends with a "#". Spaces and new lines are ignored. The series can have a "R": the Reference point for the offset.  If it is not present the reference point is the first char. If you put the reference point in the middle of the figure, make sure you make the offset smaller. If you start playing with this series you will quickly find that each part of the series is good to yield a lot of pentagons, but if you add or remove a "B" or "S" it will spoil the figure. You will notice it will cause a split that separates the figure in a part before and after the change.
 
The parameter "Order".
In the dialogue you will also find a parameter "Order" that has a start value of zero. This determines which order will be drawn. The figure with pentagons is namely self-similar. With the choice of another order you will find bigger pentagons with inscribed stars in the same pattern of lines. The line distances and the pentagons will be a factor φ bigger.