Here you can get free programs demonstrating the different types of space-time-diagrams. The Windows versions are created with Borland Delphi, those for Mac OS X are written in RealBasic. Perhaps somebody is going to create a platform-independent online version ??
Since Sept 27 of 2008 an improved version 1.1 is ready for download !
This is the type of diagram used in my book "Epstein explains Einstein". Unit legths on all axes are the same, and the axes of time and space are orthogonal. However, people used to the standard Minkowski type of diagrams will not feel comfortable with this type of diagram in the first few sessions, because an event does not correspond to a single point in spacetime! Rather, the start and the end of any process are marked by points that have the same distance in any coordinate systems. Read chapter C of my book !
LoedelP.exe ( Windows ) Loedel.app ( Mac OS X auf Intel )
This type of Space-Time-Diagram was presented in 1948 by Enrique Loedel Palumbo. In my next book I would like to show that these Loedel diagrams evolve in a quite natural way out of the Minkowski type diagrams. As long as you do not need more than 2 coordinate systems the Loedel diagrams are perfectly suited to show all the phenomena of special relativity quantitatively correct. In advantage to the Minkowski diagrams there is no need to recalibrate axes, and the symmetry of the situation (with two inertial systems) is preserved. You can easily derive the Lorentz transformations from these Loedel diagrams, and they are perfect in combination with Bondi's k-calculus.
This type of space-time-diagram was presented in 1961 by Robert W. Brehme (Am. Journal of Physics, vol. 30, p.489-496). The Brehme type diagram is mathematically equivalent to the Loedel type. Points representing an event are projected perpedicular on the corresponding axes, while in the Loedel type the projection runs parallel to the coordinate axes. In both types of diagrams space and time axes do not include a right angle. Brehme diagrams are certainly less suited to demonstrate the effects of STR. Albert Shadowitz tells us in his excellent book "Special Relativity" (Dover Publications 1968), that Brehme diagrams should be used to draw covariant vektors, where as the Loedel diagrams are ideal to show contravariant vectors.
Some hints to the above three programs. The 'hidden' functions are
a) dragging around the coordinate frames with your mouse and
b) mouseclicks in the diagram area, making the appropriate projections being calculated and drawn.
So, actually, you will not really need this introduction ...