Number Processing Patterns:
-Playing with Numbers
Basically the numbers are colour coded
(red = 1, blue =
2, yellow = 3, etc.)
Multiply and Divide:
In Multiply and Divide
the blocks are diagonally divided (two bits per
block) and numbered with maximum base
In the lower section, the blocks are
simply laid out (from one block of one -up to 6
blocks of 6) and numbered sequentially.
In the upper section, the blocks are piled up on each other
-culminating in n ^ 2 (maximum 6 x
6 = 36)
Add and Subtract:
Add and Subtract are basically "partitions"
(all the smaller numbers that a lager
number can be broken down to make the sum of the
Usually 6,1 is considered the same a 1, 6
(when partioning 7, for example)
-but in these drawings they are considered different.
The method used to generate the partitions also affect
the pattern created when all are combined -but more of this
One way of generating partitions is to take the previous
set and add one to each of the previous partitions
The new set will then need to be slightly "re-partitioned"
to fill in the missing patterns
The Basic Set of Partitions with no repetitions (i.e.
6,1 is considered the same a 1,6)
can be represented by images that look like a
bunch of Tally Sticks next to each other
When rotated, the images can represent a different
combination of Partitions.
This drawing suggests some of the possibilities
The Basic Partition Set can be represented in a Tree
(showing the transition from one partition to another)
The Extended Set (with repetitions)
is created by permutation of the elements of the Basic
An elegant way to generate the Extended Set -is to
count the potential Segmentation Points
These Segmentation Points can
then be binary coded (a cut = 1, a non-cut = 0)
-and one simply enumerates (counts) all
the binary numbers with the same number of digits as cutting
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