Variation based on a theme by dwesti

[DavidM]

After watching the animation resulting from dwesti's "bouncing line" program, I became curious as to what would happen if the lines were simply drawn and left intact instead of clearing them after a few steps. I commented out the "clearing" part of the program and ran it to see what would happen.

The result based on the parameters set up in dwesti's program yields this image:


At first glance, it's not particularly compelling. Closer inspection, though, shows a symmetric pattern is trying to emerge from the chaos. Like any good art, it invites an extended look.

This prompted me to experiment a bit more with some variations to see what would happen with various tweaks of the drawing parameters. I opted to target a 50g instead of the 48 series in order to use the bigger display. I realized that I'd have a bit more flexibility if I changed the boundary rules to check for <0 and >max instead of requiring the endpoint values to exactly match those values. This allowed me to generalize the input a bit more.

The attached program (DrawLines) runs on a 50g and takes a single argument: a list containing 9 numbers. The numbers (in order of occurrence) represent the following:

1: X1
2: Y1
3: X2
4: Y2
5: DX1
6: DY1
7: DX2
8: DY2
9: iterations

The first four arguments define the endpoints of the first line drawn. The next four arguments define the amount of offset applied to each corresponding value for the endpoints at each iteration. When an endpoint "hits" a border, the offset value is negated so that the offset is reversed for subsequent steps. The offset value is only changed when the new X/Y value would go beyond the image border, hence the bouncing effect seen in the animation. The last argument is simply a count of the lines to be drawn.

As you might expect, some of the resulting patterns aren't very interesting... simple horizontal or vertical lines, random "mashups" of lines, disconnected lines in simple patterns, etc. In other cases, the results were just the opposite. The patterns produced are sometimes amazingly artistic, even for the low resolution display on the calculator. Sometimes the final result isn't very interesting, but the animation of lines being drawn is artistic in its own way.

Here's some samples of the results obtained for the given arguments:

{ 18 60 36 18 18 -6 18 -6 750 }


{ 30 64 36 32 6 -8 6 -8 750 }


{ 39 54 78 45 13 9 13 -9 750 }



  DrawLines.zip (Size: 1.72 KB / Downloads: 5)

[DavidM]

A few more examples...

{ 16 32 16 8 -16 -4 16 4 750 }


{ 40 42 80 21 -20 7 -20 7 750 }


{ 48 48 64 32 -4 16 -4 16 750 }


{ 72 78 54 52 6 -13 6 13 750 }


This one reminds me of a simple version of something MC Escher might have done...
{ 46 35 44 28 -1 7 -1 7 750 }

[John Keith]

Those are very cool, David! They remind me of the graphics from programs published in Scientific American when Alexander K. Dewdney edited the Computer Recreations column, in the 80's I believe. Worth a look if you can find them.

[DavidM]

(12-05-2021 01:24 AM)John Keith Wrote:  Those are very cool, David! They remind me of the graphics from programs published in Scientific American when Alexander K. Dewdney edited the Computer Recreations column, in the 80's I believe. Worth a look if you can find them.

I'll try to look those up.

I'm sure that the concept of drawing repeated lines algorithmically goes back to machines and processes that pre-date computers. I would envision textile manufacturing has used similar techniques for some time.

There's quite a variety of patterns resulting from a careful selection of parameters. Here's a few more:

{ 91 12 63 48 7 -6 7 -6 750 }


{ 93 44 102 20 -3 4 -3 4 750 }


{ 96 17 120 51 12 17 -12 17 750 }


{ 96 54 104 12 -8 6 -8 6 750 }


{ 130 40 110 55 -10 5 -10 5 750 }


I promise I'll stop with these, which still only represents a subset of the interesting ones I've encountered so far. There's also some recurring themes which have occurred, including variations on certain letters (mostly "A", but also "T" and "o").

It would be interesting to see the results of similar drawings created on other platforms using similar techniques.