## Map Creativity Index ..

.. adopted in Whirly calculated as follows:
Ci = D / V, where
D - gameplay difficulty,
V - volumability. Volumability is a "boring part" of difficulty.
Raw ci would be ci = d / v, where
Raw difficulty, d = i + ( p - i ) / 5 = 0.8i + 0.2p, where
i = number of interactions between hero and other units,
p = number of moves,
p, i are taken for p - minimal solution,
v = raw volumability.
Adjusted to human difficulty, D = 0.8I + 0.2P, where
I = i - I0,
P = p - P0.
I0 = interaction base difficulty considered trivial for a human.
P0 = path base difficulty considered trivial for a human.
We take these values arbitrarily, I0 = 8, P0 = 33.
( We took number of pushes and moves from David W. Skinner [1], Map 1
making this map a point of reference for Whirly. All maps with correspondingly lesser i or p
will have ci = 0. We build the scale for adults. Kids versions need different ci. )
V = v / V0.
V0 = base volumability considered trivial for a human.
Volumability is considered as non-creative factor and is eliminated by division: d / v.
When number of boxes and walls grows, difficulty is growing, but not necessarily
demands player to be creative.
Whirling up geometrical elements without increasing of their number may contribute to
creativity ( or may not ).
There also is possible increase of creativity-demand due not only complex geometry, but
due unexpected scenario stemmed from specific geometry.
Excessively complex rules are also part of volumability.
Volumability:
v = m + 3r
mechanical complexity: m = u + s / 5 = u + ( c - u ) / 5, where
u - number of dynamic unints ( boxes, heroes ),
s - number of non-dynamic units: walls and empty spaces,
c - number of internal cells in map.
For adopted average distribution,
u u u ...
u u u ...
uWWuWWuWW...
WWWWWWWWW...
WWWuWWuWW...
....
each unit is surrounded by 5 static units.
Rules complexity, r, is counted as follows:
r = ( a - 2 ) + 3( t - 1 ), where
a - number of colonies on a map,
t - number of interaction types.
Two attributes considered as base point of complexity. If we have
less than two different types of units, just one unit, there is
"nothing" it can do at all.
Examples for maps without hero-targets:
Sokoban: a = 3, ( Colonies: hero, box, and target. )
t = 1, ( Push. )
r = 1.
Colorban: a = 3 -- 30, ( 3 races * color )
t = 1, ( Push. )
r = 1 -- 28
PullPush: a = 3 -- 30,
t = 2, ( Pull and push. )
r = 4 -- 41.
Monkeyban: a = 3,
t = 2, ( Push or push with sticky-boxes effect. )
r = 4.
Flocks: a = 3 -- 30,
t = 2, ( Push or push with sticky-boxes effect. )
r = 4 -- 41
PushMan: a = 3, ( No targets for boxes, but htarget for hero. )
r = 1.
Coefficient 3 in ( 3r ) is taken because it is a digit without corners and not very big.
Here is how we take a value for V0:
r = 1,
m = 3 + ( 14 - 3 ) / 5 = 3.22
V0 = m + 3r = 6.22
( The same map [1], Map 1 is used. )
Following model taken as a base for the formula ( p - i ) / 5.
Player has to decide to which box to move: to left or right. One brain click.
$ $
@
One hand-click, one brain-click:
$ $
@
Three hand-clicks, no brain-clicks:
@
$ $
One interaction, one brain-click:
@ $
$
This is why brain-load counted as (p-i) / 5.
***
The disadvantage of metric ci is unknown upper bound. ci allows only to order maps, not
to measure them.
CI Examples.
Circular Links:
Guest Readme
Whirly and Sokoban Variants
Project Files
## References

[1] Sokoban puzzles by David W. Skinner. Microban (155 puzzles, April, 2000)