Pasart
by Ken Wesson in 2007
Draw artistic patterns based on Pascal's triangle.
Also referred to as PasArt or PASART (all caps).
History
A first BASIC version of this artistic program is listed by Creative Computing magazine in the beginning of 1977. It explaines how it works:
Pascal's triangle is one of the most famous number patterns in mathematics. The triangle is very easy to construct. The first two rows consist of only 1's. Each of the subsequent have a 1 at either end of the row, but all other numbers in the pattern are the sum of the two numbers to the right and left in the row above.
The resulting triangle is then rotated to form a table of numbers. After that it is translated to a graphic picture built up from asterisks (*) depending on a few variables that change this behavior.
In 2007, Ken Wesson rewrote this program in assembly for the Apple-1, as he explaines:
I have just finished porting - well recoding really - one of the "games" from Creative Computing. The game is PASART, and it draws quite nice patterns generated from Pascal's Triangle. The idea is nice, and there is really a very wide range of patterns you can easily produce (I chose this one for my kid's benefit), but the original code totally ignores the inherent symmetry in the construction, and as a result is about 7 times as long as necessary! :-)
Wikipedia explaines the mathematical background on the triangle of Pascal.
Memory fix
This program starts but runs incorrect on an Apple-1 with a default memory setup. All asterisks (*) are displayed when it runs, no patterns are being drawn.
Fix it by changing the initialization of a zero-page variable in the program before running it:
308: 06 RETURN
300R RETURN
Now the program uses the start memory address $0600 (instead of $1000) for storing its bookkeeping data and draws the patterns correct.
Instructions
The program asks a four questions (explained below), hit RETURN after answering them with a number. Note that the screen of the Apple-1 is 40 characters wide and has 24 rows. The maximum amount of columns can be 39, because it needs one column for the cursor.
| Question | Description |
|---|---|
ROWS? |
Amount of rows for the drawing (>2). |
COLUMNS? |
Amount of columns (3-39). |
MODULO? |
All values of Pascal's triangle equal to 0 (zero) with this modulus are not drawn (as spaces). Others are drawn as asterisks (*). |
STYLE (1,2,3)? |
Three choices for the style of the drawing: 1) a single triangle starting at the top left corner, 2) two triangles starting at opposite corners and 3) four triangles starting in all corners. |
The drawing will be generated and displayed on the screen after answering all questions. Press RETURN to create another drawing or hit ESC to exit the program.
References
- Personal website of Ken Wesson, this program is part of the Samples-file for Krusader. A few sample patterns can be found here as well.
- Creative Computing (March-April 1977, volume 3, no. 2, p. 122-123) published a BASIC version of this program, which was used as an inspiration for this version for the Apple-1.
- Watch a YouTube video of the program in action.
- Pascal's triangle explained on Wikipedia.
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