https://blogs.lotterypost.com/jadelottery/2016/9/combinatorial-fractalization-reformated.htm JADELottery's Blog: Combinatorial Fractalization reformated en-us Lottery Post RSS Generator https://blogs.lotterypost.com/jadelottery/2016/9/combinatorial-fractalization-reformated.htm https://blogs.lotterypost.com/jadelottery/2016/9/combinatorial-fractalization-reformated.htm Tue, 20 Sep 2016 02:35:53 GMT JADELottery A while back we post the Combinatorial Fractalization.

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We reformatted it for other browsers.

Combinatorial Fractalization

C(n, r) = [from z = 1 to z = n - r + 1] Σ C(n - z, r - 1)

C(n, r) = C(n - 1, r - 1) + C(n - 2, r - 1) + C(n - 3, r - 1) + ... + C(r + 3, r - 1) + C(r + 2, r - 1) + C(r + 1, r - 1) + C(r, r - 1) + C(r - 1, r - 1)

Fractals of C(n, r) - {C(n - 1, r - 1), C(n - 2, r - 1), C(n - 3, r - 1), ... , C(r + 3, r - 1), C(r + 2, r - 1), C(r + 1, r - 1), C(r, r - 1), C(r - 1, r - 1)}

Fractals of C(n, r) - [from z = 1 to z = n - r + 1] {C(n - z, r - 1)}

Iteration of C(n, r) Fractals

Fractals of C(n - 1, r - 1) - {C(n - 2, r - 2), C(n - 3, r - 2), C(n - 4, r - 2), ... , C(r + 2, r - 2), C(r + 1, r - 2), C(r, r - 2), C(r - 1, r - 2), C(r - 2, r - 2)}

Fractals of C(n - 1, r - 1) - [from z = 1 to z = n - r + 1] {C(n - z - 1, r - 2)}

Fractals of C(n - 2, r - 1) - {C(n - 3, r - 2), C(n - 4, r - 2), C(n - 5, r - 2), ... , C(r + 2, r - 2), C(r + 1, r - 2), C(r, r - 2), C(r - 1, r - 2), C(r - 2, r - 2)}

Fractals of C(n - 2, r - 1) - [from z = 1 to z = n - r] {C(n - z - 2, r - 2)}

Fractals of C(n - 3, r - 1) - {C(n - 4, r - 2), C(n - 5, r - 2), C(n - 6, r - 2), ... , C(r + 2, r - 2), C(r + 1, r - 2), C(r, r - 2), C(r - 1, r - 2), C(r - 2, r - 2)}

Fractals of C(n - 3, r - 1) - [from z = 1 to z = n - r -1] {C(n - z - 3, r - 2)}

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Fractals of C(r + 1, r - 1) - {C(r, r - 2), C(r - 1, r - 2), C(r - 2, r - 2)}

Fractals of C(r + 1, r - 1) - [from z = 1 to z = 3] {C(r - z + 1, r - 2)}

Fractals of C(r, r - 1) - {C(r - 1, r - 2), C(r - 2, r - 2)}

Fractals of C(r, r - 1) - [from z = 1 to z = 2] {C(r - z, r - 2)}

Fractals of C(r - 1, r - 1) - {C(r - 2, r - 2)}

Fractals of C(r - 1, r - 1) - [from z = 1 to z = 1] {C(r - z - 1, r - 2)}

Within every combinatorial set there are subsets of combinations that are similar in characteristics to the whole combination. Example, below is a sample combinatorial set of 8 numbers taken 6 at a time. Alongside the combinatorial set are a few subsets of combinations. Table 1 shows only one leg of the fractal path. The fractals are in red and transformed to the right. The symbol Ψ is the superset fractal and extends to infinity.

Table 1

Fractal Path is Ψ (8,6) (7,5) (6,4) (5,3) (4,2) (3,1)

1

2

3

4

5

6

1

2

3

4

5

1

2

3

4

1

2

3

1

2

1

1

2

3

4

5

7

1

2

3

4

6

1

2

3

5

1

2

4

1

3

2

1

2

3

4

5

8

1

2

3

4

7

1

2

3

6

1

2

5

1

4

3

1

2

3

4

6

7

1

2

3

5

6

1

2

4

5

1

3

4

2

3

1

2

3

4

6

8

1

2

3

5

7

1

2

4

6

1

3

5

2

4

1

2

3

4

7

8

1

2

3

6

7

1

2

5

6

1

4

5

3

4

1

2

3

5

6

7

1

2

4

5

6

1

3

4

5

2

3

4

1

2

3

5

6

8

1

2

4

5

7

1

3

4

6

2

3

5

1

2

3

5

7

8

1

2

4

6

7

1

3

5

6

2

4

5

1

2

3

6

7

8

1

2

5

6

7

1

4

5

6

3

4

5

1

2

4

5

6

7

1

3

4

5

6

2

3

4

5

1

2

4

5

6

8

1

3

4

5

7

2

3

4

6

1

2

4

5

7

8

1

3

4

6

7

2

3

5

6

1

2

4

6

7

8

1

3

5

6

7

2

4

5

6

1

2

5

6

7

8

1

4

5

6

7

3

4

5

6

1

3

4

5

6

7

2

3

4

5

6

1

3

4

5

6

8

2

3

4

5

7

1

3

4

5

7

8

2

3

4

6

7

1

3

4

6

7

8

2

3

5

6

7

1

3

5

6

7

8

2

4

5

6

7

1

4

5

6

7

8

3

4

5

6

7

2

3

4

5

6

7

2

3

4

5

6

8

2

3

4

5

7

8

2

3

4

6

7

8

2

3

5

6

7

8

2

4

5

6

7

8

3

4

5

6

7

8

Here's another fractal path shown in Table 2.

Table 2

Fractal Path is Ψ (8,6) (7,5) (5,4) (3,3) (2,2) (1,1)

1

2

3

4

5

6

1

2

3

4

5

1

2

3

4

5

7

1

2

3

4

6

1

2

3

4

5

8

1

2

3

4

7

1

2

3

4

6

7

1

2

3

5

6

1

2

3

4

6

8

1

2

3

5

7

1

2

3

4

7

8

1

2

3

6

7

1

2

3

5

6

7

1

2

4

5

6

1

2

3

5

6

8

1

2

4

5

7

1

2

3

5

7

8

1

2

4

6

7

1

2

3

6

7

8

1

2

5

6

7

1

2

4

5

6

7

1

3

4

5

6

1

2

4

5

6

8

1

3

4

5

7

1

2

4

5

7

8

1

3

4

6

7

1

2

4

6

7

8

1

3

5

6

7

1

2

5

6

7

8

1

4

5

6

7

1

3

4

5

6

7

2

3

4

5

6

1

2

3

4

1

3

4

5

6

8

2

3

4

5

7

1

2

3

5

1

3

4

5

7

8

2

3

4

6

7

1

2

4

5

1

3

4

6

7

8

2

3

5

6

7

1

3

4

5

1

3

5

6

7

8

2

4

5

6

7

2

3

4

5

1

2

3

1

2

1

1

4

5

6

7

8

3

4

5

6

7

2

3

4

5

6

7

2

3

4

5

6

8

2

3

4

5

7

8

2

3

4

6

7

8

2

3

5

6

7

8

2

4

5

6

7

8

3

4

5

6

7

8

... [ More ]

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