Lighthouse Simulation Program
Tips, Tricks & Other Interesting and Weird Things

Tips & Tricks

• For fast production/reproduction of images, have only Connect Points, Smart Seek, and Smart Track checked in the check boxes. The step angle should be as small as required to give adequate detail. The small the step angle, the longer it takes to draw.

• For observing exactly how the path is drawn, or demonstrating to others, don't use Smart Seek, but enable Show Rays and Show Labels. You may wish to incorporate a delay too to slow it down (about 100 ms) or also step through the trace, using the Step from Start feature.

• You can pause the simulation at any point, by pressing the P key. Once in pause mode, you may press P again to unpause it, or press S to step through the trace one step-angle at a time.

• You can capture the image once the screen is drawn if you are running under windows. To do this, press <Alt>+<Enter> when the image has been drawn.
  This will take you back to Windows, but the program will be running in a window.
  If necessary, drag the bottom right hand corner of the window out to see the whole picture.
  Then press <Alt>+<Print-Screen>. This will capture the picture into the clipboard. You may then paste it into a program such as Microsoft Word, WordPad, or Paint, to edit or print it.

Interesting Observations

The following are observations which have some underlying mathematical reason for them. What that reason is, well, is probably fairly complicated, but there is some.

• If B is constant at 1, as A multiplier increases, each successive odd increment, a new curve is drawn, ie 1:1 & 2:1 = 1 curve, 3:1 & 4:1 = 2 curves, 5:1 & 6:1 = 3 curves, etc.

• If one multiplier is negative, and the other positive, (ie, both lighthouses in same directions, but still start facing each other) patterns similar to magnetic flux lines are created. Try -21 and 20, step angle 0.1.

• Using the same thing as above, but having both positive, will create an effect similar to the magnetic flux lines produced when two like poles of a magnet are in close proximity. (eg, try 20 to 21)

Weird Things

The following use the Join curves feature, which mathematically does nothing, as the curves theoretically reach off to infinity, but make some nice drawings. If you're looking for the maths in them, there's isnt any.

• Set Join curves & when offscreen. Ratio of 7:1..... is it a martian or a person with a top hat?

• Echidna - same as above but try 20:1

• Pihrana - same as above but try 3:2. Other ratios such as 4:3 7:6, 19:18, etc. give some neat symmetrical pictures.

If you discover any other odd, weird, interesting or mathematically intriguing images using a range of variables, and would like to have them up on here, please send them to Bernard Blackham.

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Written by Bernard Blackham
© 2000