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This is the .ARC file containing the graphics program ST GIZMO By Helge Skjeveland 1466 S. Main Orem, UT 84058-7482 Tel.: (801)224-8483. This program is not freeware, but SHAREware. I am asking for $10 if you keep this program for subsequent use. Commented LDW BASIC source code and a detailed explanation (implementation notes) are available for an additional $15. This .ARC file may be freely distributed via any BBS, or via diskette. Please keep this README.DOC and STGIZMAN.DOC with STGIZMO.PRG so that others may have the documentation and I get the $10 from the kind souls who believe in paying for what they use. Thanks. -------------------------------------------------------------------------------- ST GIZMO MANUAL ST GIZMO is a graphic-generating program. It will allow you to create many interesting designs. It is designed to allow you to take a snapshot (e.g., using SNAPSHOT.ACC, which is available with the GST's 1ST WORD PLUS) of the screen, whence you can integrate the designs with your graphics pack- ages. It is a fully implemented GEM application (GEM is a trademark of Digital Research, Inc.). The following combined manual and tutorial will both enable you to use the product and explain the theory behind it. If you're like the author, you won't even read the instructions, but just forge ahead and experiment, which is OK, since you can't damage the com- puter or program by doing so; however, this is not a long manual, so when you're through, come back and read through it: You will get far more pleasure out of the money you paid if you do so. The program is, for your convenience, not copy protected; but please, don't pirate it. I earn my living programming, and I am just as poor as most of you out there. To you 99% who paid for this program, thanks. I have tested this program thoroughly, but if you find any problems, drop me a note, and I'll fix it. Enjoy!! Let's try ST GIZMO out: Invoke STGIZMO (by clicking on the STGIZMO.PRG icon. You will see a dialog box appear that has various fields. For now, just click on DONE (or hit RETURN -- as with all GEM buttons, if it has a thick border, striking RETURN will select it, just as if you clicked on it [this is called a "radio button"]). Then click on OK (strike RETURN) when the TERMINATE DIALOG alert box appears. You will now see the rotating heptagram (seven-pointed star) default pattern. Interesting and beautiful patterns like this are easy to generate with ST GIZMO. Now click on the close box in the upper left corner of the window, or select **QUIT** from the FUNCTIONS menu, and answer YES to the alert box. You are now back at the Data Entry dialog box. You can exit the program from here by clicking on the EXIT box. Since this has a skinny border, you can only exit by deliberately selecting it (a safety feature). ST GIZMO is driven by parametric equations in two dimensions. What this means is that there are two oscillating functions, one in the vertical, the other in the horizontal. By modifying their initial size (scale), decay rate, period, and phase it is possible to generate many interesting patterns. By intelligently selecting the increment and choosing either draw or plot mode it is possible to vastly increase the number and variety of generatable patterns. ST GIZMO is compatible with all three ST reso- lutions, but make sure that if you are going to incorporate your ST GIZMO pattern with a preexistent graphic that you use the same resolution for both the pattern and graphic (you cannot mix resolutions -- it's like cramming a square peg into a round hole . . . it won't work). For the purpose of the following examples, set the DECAY to a huge number, say, 16E11 (one point six trillion, the national debt). This will prevent the figure from shrinking while it draws, so that the actions will be clear. On to the instructions: The Data Entry dialog box functions are: X:Y period ratio -- this determines how many times an oscillation in one direction (X=horizontal) will occur for an oscillation in the other direction (Y=verti- cal). If you use 1:1, a phase angle 90 degrees, and a small increment, you will get a circle. This is because sin(t + 90)=cos(t), so you get the parametric equation /x=sin(t) \y=cos(t), a circle. phase (phi) -- If you change the phase to 0, then you have the parametric equation /x=sin(t) \y-sin(t). Since x and y are doing the same thing, you get an unexciting diagonal line. If you use phase=45, then you get a nice ellipse with aspect ratio 2:1 (since 90:45=2:1). To get an ellipse of aspect 3:1, use 30 degrees (90:30= 3:1), and so on. increment (theta)-- This specifies how big the angle increment you want STGIZMO to increase by each time it draws or plots. If you use phase 90 and 1:1 ratio and use a small increment (say, five degrees), then you will get what appears to be a circle; but since a circle is a continuous set of points equidistant from the center, and a computer can only deal in fixed increments, you are really generating a polygon of 72 sides (but THAT many sides LOOKS like a circle). If you choose an increment of 90, you will get a diamond (rhombus). This is, of course, a polygon of four sides. 120 generates an equilateral triangle, since 360/120=3. To get a pentagon, use 72 degrees (360/5=72). Now try something interesting: use 144 degrees (144 = 2 x 72). You now have a five-pointed star, a pentagram. This results because you are SKIPPING every other vertex that would've resulted if you used 72 degrees (for, 144 = 2 x 72, see?). The increment for the heptagon (seven-sided polygon) is 51.4285 (~360/7). Note that all the seven-sided figures will appear to rotate slightly because seven will not divide evenly into 360. If you want them to be more stable, use a calculator (desk accessory or hand-held) to get a more precise value for the increment(s), up to the maximum the field size will allow. There is only one possible pentagram, but there are TWO possible unique heptagrams: one uses the increment 102.8571 (2 x 51.4285), and skips every OTHER vertex; the other uses 153.257 (3 x 51.4285), and skips TWO vertices each time. The nonagon (nine sides) is generated by 360/9=40. There are three possible nonagrams (enneagrams), two of which can be generated by STGIZMO: 80, where every other vertex of the nonagon is skipped; and 160, where FOUR vertices are skipped. The remaining one is 120, which would be three inter- laced equilateral triangles (3 x 3 = 9). Since the computer can't draw these without "lifting its pen up," as it were, we can't directly generate it. If you want to, make and snapshot the three separate triangles, then overlay them onto each other in a graphics pack- age using transparent mode. If the number of vertices is not a prime number, there will still be polygrams, but some will consist of interlaced polygons (i.e., nine can be factored into 3 x 3 -- three interlaced equilateral triangles). Another interesting example of this is the octagram (8 sides): An octagon is generated by the increment 45 degrees. Of course, you will remember that 2 x 45 = 90 degrees generated a rhombus. That octagram is an interlaced rhombus and square, thusly (crude): /\ -------- |/ \| /| |\ \| |/ |\ /| -------- \/ Since two divides evenly into eight, we have two distinct, interlaced polygons. You can make this by snapshot/overlay techniques, too. A continuous octagram is generated by using 3 x 45, which is 135 degrees, since 3 doesn't divide evenly into 8. Happy exploring! decay rate (delta)--The larger the decay rate, the slower the decay. We set this to 16E11 (one point six trillion), which makes for imperceptible shrinkage. If you use, say, 500 (as in the default heptagram), the figure will slowly shrink. If you use an angular increment that is slightly smaller or larger than will evenly divide into 360, then the polygon or polygram will shrink and rotate simultaneously, generating beautiful patterns (especially for you fortunate monochrome monitor owners!). draw scale (sigma)--100% means full size, but if you want it smaller, you can shrink its initial size, and it will shrink far- ther from that point. You can also specify a larger size than the full window (>100%): the pattern will be clipped and shrink until it becomes visible, and thence shrink as far as you desire. If you make the scale too large, you may not be able to see the pattern for a while, because the screen will be smaller than the central hole! If your decay rate is set small enough, and you wait, though, the pattern will eventually show itself. DRAW button --A line is drawn between successive positions. PLOT button --Each successive position is plotted only. DONE radio button --Terminate the dialog and go to display mode. EXIT button --**QUIT** ST GIZMO DISPLAY MODE: In this mode the mouse arrow will eventually become invisible if you do not move it; however, moving it at all makes it reappear. CLOSE BOX (upper left-hand corner of the window): clicking here is the same as clicking on the **QUIT** menu option. WINDOW TITLE BAR: Indicates display attributes (drawing, plotting, or paused) MENUS: The menu becomes available the first time you run a pattern dis- play. ATARI/DESK-- ABOUT STGIZMO --program author's info DESK ACCESS --You can invoke desk accessories here. You can, for example, use a calculator accessory to find the values to experiment with for entry into the dialog box; or you can take snapshots of a pattern for use with a graphics package, desktop publishing, etc. ***NOTE: WHEN YOUR MOUSE LEAVES THE DISPLAY WINDOW, THE PROGRAM WILL BE PAUSED. FOR YOUR CONVENIENCE IT IS LEFT TO YOU TO RESTART IT, IF DESIRED. TO DO SO, CLICK ON PAUSE IN THE MENU TO TOGGLE THE DISPLAY ACTIVITY ON AGAIN. FUNCTIONS -- PAUSE --automatically activated if your mouse pointer leaves the display window. Click on it to resume drawing. RERUN --erases the pattern and re-runs it. If nothing happens, remember to check that PAUSE is not on (window title and checked PAUSE menu entry). **QUIT** --asks you "ARE YOU SURE?", if so, click on YES or press RETURN to access the Data Entry dialog. If you want to terminate ST GIZMO altogether, click on the EXIT button in the Data Entry dialog: That is the only EXIT point. You can also **QUIT** to the dialog box by clicking on the window's close box (upper left corner). More about patterns: If you use other than 1:1 in the ratio fields, you will get complex patterns called Lissajous patterns (after the Frenchman who first studied them). 1:2 will give a portion of a parabola, 2:1 will give the same rotated 90 de- grees. Using various increments with Lissajous patterns and PLOT mode will create VERY slow but gorgeous patterns that have a three-dimensional appear- ance. For example, try ratio 1:2 phase 90 increment 153 decay 3000 scale 100 PLOT mode or ratio 101:100 phase 90 increment 2 decay 16e11 scale 100 DRAW mode and don't stay up all night! (I did, sometimes, while making STGIZMO) *** END OF FILE ***