Angry Birds Calculator Program?

Here’s a little program I wrote for the TI-83 during the NW Math Conference last month, during the session just before my own.  It could serve a number of possible functions, including introducing programming to students, motivating a lesson on sine and cosine, or motivating a lesson on parabolas (though the program doesn’t use quadratic functions).
It’s not particularly rewarding to play, but maybe you can improve on it – right now it does three things:

• draws a pig at a random distance
• asks for angle and “force”
• plots points until they go off the screen

There’s no collision detection or points system, and no end to the game, but what can you do?Here’s a look at the code so you can make your own improved version if you’re so inclined:

//FIRST, THE SETUP

• Lbl B
• ClrDraw
• AxesOff
• Degree
• PlotsOff
• FnOff
• 10→Xmax:10→Ymax
• -2→Xmin:-2→Ymin

//NEXT, THE SCENE

• rand*4+4→P 
  (random number between 4 and 8 for the pig’s x-coordinate)
• Line(-2,-1,10,-1) 
  (the ground)
• Line(0,-1,0,0)
  (the slingshot)
• Circle (P,0,1) 
  (this represents the pig. I made a more detailed pig face since I had some extra time, which I’ve included at the bottom).

//SET SOME STARTING VALUES

• 0→X:0→Y 
  (starting values for plotting the bird path)
• -0.07→G 
  (acceleration due to gravity… units are arbitrary, so I just tweaked this until it looked good)
• Pause: ClrHome
• Disp “ANGLE?”: Prompt T
• cos(T)→D: sin(T)→E 
  (D and E will tell us the x and y increments for the bird’s path)
• Disp “FORCE (1-10)?”: Prompt F
• F/10*D→D: F/10*E→E
  (D and E are scaled by 1/10 of the “force” …also arbitrary)

//PLOT SOME POINTS

• Lbl A
• Pt-On(X,Y)
• X+D→X: Y+E→Y
  (If D and E both remain constant, the bird will go in a line.  The curve is produced by changing E, the increment for y.)
• E+G→E
  (You could think of E as velocity and G and acceleration)
• If Y>0 and X<10: Goto A
  (Keep plotting points until you go off-screen to the right or hit the ground)
• Pause
• Goto B
  (New pig!)

//THAT’S IT!  If you want a more detailed pig, replace the Circle command with the following (I got rid of the circle because it takes so long to plot):

• Line(P-1,0,P-0.5,1)
• Line(P-0.5,1,P+.5,1)
• Line(P+0.5,1,P+1,0)
• Line(P+1,0,P+0.5,-1)
• Line(P+.5,-1,P-0.5,-1)
• Line(P-0.5,-1,P-1,0)
  (This forms a hexagon for the pig’s head)
• Line (P+0.4,0.1,P+0.4,-0.7)
• Line(P+0.4,-0.7,P-0.4,-0.7)
• Line(P-0.4,-0.7,P-0.4,0.1)
• Line(P-.4,0.1,P+0.4,0.1)
  (This forms a rectangle nose)
• Pt-On(P+0.5,1.2,2): Pt-On(P-0.5,1.2,2)
  (Ears are points with “style 2” so they’re tiny squares)
• Pt-On(P+0.5,0.5,3): Pt-On(P+-0.4,0.5,3)
  (Eyes have “style 3” so they’re tiny crosses)
• Pt-On(P-0.15,-0.3): Pt-On(P+0.15,-0.3)
  (Nostrils!)

Mandelbrot’s birthday pancake

Growing plants

Leafing through a magazine the other day, I happened across this page:

I wondered how many plants they’d have the next year.  With limited information, what would a best guess look like?  With only three points, you can use a variety of functions to predict the next one – which function makes the most sense?  The only other information we have is that the person quoted is evidently a professional gardener.