Another Look at 2068 Graphics: More or Less

Listings #1 and #2 are shown to illustrate but one point. Both are graphically interesting, though this was not my full intention by including them.

Often what is most important when one does mathematically generated graphics is speed. Many take the 2068 the better part of an hour to produce — a long time to wait if one is testing and debugging formulas. One common trick is to change STEP values in FOR/NEXT loops to larger numbers. This lets a programmer “skip the detail” and more quickly get an idea of the general outcome. For the final version, such values can be altered back so as to show the detail again.

I have found, however, that we tend to overwork our computers when generating graphic displays. The T/S 2068 knows no fatigue. It will calculate cos .4 five thousand times during a graphic without a complaint. But couldn’t the value of cos .4 (.92106099) just as easily have been plugged in and thus saved some time plotting the graphic?

The more calculations the 2068 is forced to do each go, the slower and less appealing our graphic is to watch. Listing #1A produces a “bouncing ball”. Listing #1B does exactly the same thing only less work. Note the math in lines 180 and 190 of listing #1A have been reduced to line 20 of listing #1B. All the variable calculations in lines 10, 20, and 30 of #1A were also eliminated. These should both be run and compared for speed. Listing #1B will go even faster if line 30 is changed to read simply: PLOT x,y.

Listings #2A and #2B are mathematically much more complex. Again both produce the same sort of graphic. Listing #2A abounds in variables and is replete with other formula “fat”. Most certainly the formulas in this listing should be worked through and understood by the programmer. In the final version such length is of no use to the computer — simply more code it must wade through. Listing #2B is a version with nearly every calculation trimmed down.

Listing #2B is a fun one for experimentation. The slightest variation will cause differing outcomes. The beauty and the excitement can only be achieved through experimenting, but some examples include:

• Changing the value multiplied by z in line 120 adjusts the height of the topography — .3 is flatter, .8 is steeper, 2.0 is pretty strange. The value 600 shown in lines 100 and 120 can be increased for larger scale, decreased for smaller.
• The value for b in line 90 is negative. The more negative it becomes the more exaggerated the right portion of the display becomes.
• As discussed earlier, a smaller STEP value in line 60, the closer and more detailed the plotting becomes (and slower, too).

One might now take a look back through some old terribly slow graphic programs laying around. One will be amazed at the excess work we have been forcing out of our 2068s. Next time we will look into some even more interesting graphic ideas.