compact pattern

Patterns {compact pattern} can have only points, which connect horizontally or vertically to at least one other point.

value

Patterns have numerical values.

boundary

Unique patterns have unique boundaries and surfaces. If surface has value, pattern has value, and vice versa.

differences

Changing one pattern to another adds or subtracts one point.

number

Same number of points has same number of patterns. 1 point has 1 possible pattern. 2 points have 1 possible pattern. 3 points have 2 possible patterns. 4 points have 5 possible patterns. 5 points have 12 possible patterns. 6 points have 35 possible patterns. 7 points have 108 possible patterns. 8 points have 369 possible patterns. 9 points have 1285 possible patterns. 10 points have 4655 possible patterns. 11 points have 17072 possible patterns. 12 points have 63565 possible patterns. 13 points have 238299 possible patterns.

number: multiples

Multiple for each step is 1, 2.00, 2.50, 2.40, 2.92, 3.09, 3.41, 3.48, 3.62, 3.67, 3.72, and 3.75. Multiple for odd steps is 2, 6, 9, 11.89, 13.29, and 13.96. Multiple for even steps is 5, 7, 10.54, 12.61, and 13.66.

factoring

Pattern-number factors are 1*1, 2*1, 5*1, 3*2*2, 7*5, 3*3*3*2*2, 41*3*3, 257*5, 19*7*7*5, 97*11*2*2*2*2, 12713*5, and 79433*3.

point types

Patterns can have different point types, such as colors. For three point types, 1 point has 3 possible patterns. 2 points have 6 possible pattern. 3 points have 36 possible patterns. 4 points have 246 possible patterns. 5 points have 2115 possible patterns. Multiple for each step is 2.00, 6.00, 6.83, and 8.60. Multiple for odd steps is 12 or 58.75. Multiple for even steps is 41. Pattern-number factors are 3*1, 3*2, 3*2*2, 41*3*2, and 47*5*3*3.

transformations

Pattern translation, reflection, rotation, and inversion make same pattern.

diagonals

If points can connect diagonally, patterns are not fundamentally different, only less compact. Patterns with points connected diagonally can transform to connect only horizontally or vertically. For example, V is L rotated 45 degrees.

Whole Section in One File

3-Computer Science-System Analysis-Patterns

Drawings

Technical Information

Date Modified: 2022.0224

compact pattern

Related Topics in Table of Contents

Whole Section in One File

Drawings

Contents and Indexes of Topics, Names, and Works

Searching

Database Information, Disclaimer, Privacy Statement, and Rights

References and Bibliography

Technical Information