The BITPICT Computation System Sample Rule Sets

1
The BITPICT Computation System- Sample Rule
Sets -

• to Accompany Video
•  
• George W. FurnasSchool of Information and
  College of Engineering
  
• University of MichiganAnn Arbor, MI 48103-1092
• furnas_at_umich.edu 

2
Introduction

• What follow are various rules that figure in
  several of the systems seen in the BITPICT
  videos, and available in as MPEGS at
  
• http//madison.si.umich.edu/BITPICT.MPEGS/
• (In some cases all the rules are given. In others
  there are just example rules from a larger set.)
  
  
• Note For a system of rules to run properly one
  must also specify what sort of conflict
  resolution scheme will be used, and any explicit
  priorities that individual rules must have.

3
Rule Transformation (Symmetries) Key

• These little symbols, placed underneath the rule
  arrows, show what geometric transformations the
  matcher is supposed to consider when looking for
  matches. 
• X Translation only
• Y Translation only
• Rotation only
• Reflection about Y only
• Reflection about X only
• XY Translation only
• XY Translation and Rotation
• XY Translation and Reflection about Y
• XY Translation and Reflection about X
• XY Translation and Reflection about X and Y
• XY Translation and Reflection and Rotation

E.g.,
Means Match (and apply) this rule at - a
ll XY values - all rotations - all reflectio
ns
4
Rules for Count Connected Components - 1

• Rules to nibble tips (complete)
• Straight Tips L- Tips
  T-Junction Tips
  
• Rules to Move Dots to Lower Right Corner
  (complete)
  
• "Falling Snow" Drift Right 

5
Rules for Count Connected Components - 2

• Rules for Roman Numerals (sample)
• Dot to "I" Five Is to one V
• Two Vs to one X

6
Rules for Find Longest Stick - 1                 
                                                  
                                               (co
mplete)

• Rules to Make Green Sticks Fall
• Bottom pixel falls Next pixel move down
  to close                                       
  the gap
  
• Rules to Make Blue Pointer-Bar Fall
• Bottom pixel falls Next pixel move down
  to close                                       
  the gap 
  

7
Rules for Find Longest Stick - 2

• Rules for Highlighting Success
• Begin Highlight at collision of bar and stick
  pixels
  
• Propagate Yellow Propagate Red
  (down stick) (along
  rod)
  
• Propagate Red across gap (to the Scale)  

8
Rules for Balls and Ramp                         
                                                  
                                        (complete)

• Rules to Make Balls Fall
• Ball with one pixel of space below it ...falls
  down one pixel
  
• Ball against ramp segment with space below and
  beside ... moves down and to the side
  

(Rules date from BW   bitpict era.
Later,   colors would have   been used to
  differentiate Ball   from Ramp.)
Two Ramp Pixels
9
Rules for Maze Walker                            
                                                  
                                     (complete)

• Rules for walker to move, leaving "chalk-line"
• Walker one pixel away from three-pixel wall and
  with two empty spaces ahead...moves into one of
  them leaving a chalk line behind.
  
• Walker, coming to outside corner, ...takes
  several steps at once to go around it. 
  

Maze Wall (3pixels wide)
Maze Walker
(Rules date from BW bitpict era.
Later, colors would have been
used to differentiate Walker
from Wall.)
10
Rules for Logic Gates ("revisited") -
1a                                               
                                                  
                (complete)

• Rules to Propagate Voltage Transitions
• Leading edge (white) of High moves forward,
  wiping out Low (light gray) and leaving behind
  High (yellow)
  
• Similarly, a leading edge (dark gray) of Low
  moves forward, wiping out High (yellow) and
  leaving behind Low (light gray)
  

11
Rules for Logic Gates ("revisited") - 1b

• Rules to Propagate Voltage Transitions (cont.)
• Rule to take leading edge High across gap (black)
  and overlapping wire of indeterminate color
  (zigzag)
  
• Similar rule to take leading edge Low across gap
  (black) and overlapping wire of indeterminate
  color.
  
• Rules for gates (green) to absorb leading edge
  transitions 

ZigZag (dont care)
ZigZag (dont care)
12
Rules for Logic Gates ("revisited") - 2

• Rules for Logic Gates themselves
• NOT gate NOT(0)1 NOT gate NOT(1)0
• AND gate 010 OR gate 011 
• AND/OR gate 0?00 AND/OR gate 1?11

Dk.Gray (leading edge low)
ZigZag (dont care) around center of these two
rules lets it match both AND and OR gates
13
Rules for Logic Gates ("revisited") - 3

• Rules for Digital readout
• Wrong digit O (or 1) over Hi (or Lo) wire
  ...gets corrected
  

14
Rules for A to B around Obstacle - 1


                                   
                                                  
                              (complete)

• Rules to Grow the Buffer Zone around the
  Obstacle
  
• Background (lavender) pixel next to Obstacle
  pixel (white) ...turns Red1 
  
• Background (lavender) pixel next to Red1 pixel
  (white) ...turns Red2
  
• Similarly, for Red3-Red6

15
Rules for A to B around Obstacle - 2

• Rules to Grow the Distance Field (mod 3) around
  "B"
  
• A background (lavender) pixel next to "B" pixel
  (light blue) ...turns Dark Blue
  
• A background (lavender) pixel next to Dark Blue
  pixel ...turns Green
  
• A background (lavender) pixel next to Green pixel
  ...turns Mustard
  
• A background (lavender) pixel next to Mustard
  pixel ...turns Dark Blue, forming a cycle of
  colors.
  

16
Rules for A to B around Obstacle - 3

• Rules for Walker to Climb Down Distance Field
  Gradient (basic)
  
• Dark color beside pastel color of previous color
  in cycle ...changes to its pastel version.
  
• Rules to cleanup infrastructure colored pixels
  (in video but not in MPEGS)
  
• Buffer and distance field colors ...change back
  to background color (lavender)
  

17
Rules for Paint THE END - 1

(complete)

• Paint flow propagation (high priority).
• Rules to Move Paint Brush
• Paintbrush moves left

18
Rules for Paint THE END - 2

• Rules to Move Paint Brush (cont.)
• Paintbrush over boundary to unpainted area
  ...pierces boundary
  
• Piercing Paintbrush over painted area
  ...retracts.