New example program: draw a fractal tree (#152)

* demo of prog8 recursion to draw a fractal tree

* feat: comments

* fix: comment formatting

* feat: make minimum branch size a tunable parameter

examples/fractal-tree.p8

@@ -0,0 +1,79 @@
+; Draw a fractal tree recursively
+; This is an example of doing recursion with local per-call state that has to
+; be preserved across recursive calls, as opposed to queens.p8 where the
+; recursive function only modifies global state.
+;
+; Note: this program can be compiled for multiple target systems.
+%import floats
+%import graphics
+%zeropage basicsafe
+
+main {
+     ; Adjust these parameters to change the appearance of the tree:
+     ; 1. the angle of each branch away from its parent (left and right)
+     const float delta_theta   = floats.π / 6
+
+     ; 2. the size of each branch relative to its parent
+     const float shrink_factor = 2.0 / 3.0
+
+     ; 3. the size of the smallest branch (in pixels)
+     const float minimum_branch = 1.0
+
+     ; These stacks hold copies of the parameters during recursive calls
+     uword[11] x
+     ubyte[11] y
+     float[11] theta
+     float[11] length
+
+     ; This points to the current level of stack in use
+     ubyte stack_pointer
+
+     ; draw a branch starting at (x1, y1) at angle th1 with length len1
+     ; recurses if length is large enough
+     sub draw_branch(uword x1, ubyte y1, float th1, float len1) {
+
+         uword x2 = (x1 as float + len1 * floats.cos(th1)) as uword
+         ubyte y2 = (y1 as float - len1 * floats.sin(th1)) as ubyte
+         graphics.line(x1, y1, x2, y2)
+
+         if len1 >= minimum_branch {
+             ; push parameters onto stacks
+             x[stack_pointer] = x1
+             y[stack_pointer] = y1
+             theta[stack_pointer] = th1
+             length[stack_pointer] = len1
+             stack_pointer += 1
+
+             draw_branch(x2, y2, th1 - delta_theta, len1 * shrink_factor)
+
+             ; recover parameters after recursive call
+             x1   = x[stack_pointer - 1]
+             y1   = y[stack_pointer - 1]
+             th1  = theta[stack_pointer - 1]
+             len1 = length[stack_pointer - 1]
+
+             x2 = (x1 as float + len1 * floats.cos(th1)) as uword
+             y2 = (y1 as float - len1 * floats.sin(th1)) as ubyte
+
+             draw_branch(x2, y2, th1 + delta_theta, len1 * shrink_factor)
+
+             ; pop stack level
+             stack_pointer -= 1
+         }
+     }
+
+     sub start() {
+         graphics.enable_bitmap_mode()
+
+         draw_branch(graphics.WIDTH / 2, graphics.HEIGHT - 1,
+                     floats.π / 2,
+                     graphics.HEIGHT / 2 * shrink_factor)
+
+
+         ; done rendering; wait for a key before exiting
+         do {
+             ubyte key = cbm.GETIN2()
+         } until key != 0
+         graphics.disable_bitmap_mode()
+     }
+}