Attack Scaling Patterns

1. The "Self-Generating" Pattern

• Start: 2, 3

• Branching off 2:

  • $4 = \mathbf{2} \times 2$

• Branching off 3:

  • $6 = \mathbf{3} \times 2$
  • $9 = \mathbf{3} \times 3$

• Branching off 6:

  • $12 = \mathbf{6} \times 2$
  • $18 = \mathbf{6} \times 3$

• Branching off 12:

  • $24 = \mathbf{12} \times 2$
  • (Next would be: $36 = \mathbf{12} \times 3$)

Every time a number is generated by a $\times 2$ operation ($3, 6, 12$), it becomes the new foundation for the next pair of numbers—first multiplied by 2, then by 3.

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2. The "What if 9 was an 8?" Interleaved Doubling Pattern

If you swap $9 \rightarrow 8$, and naturally shift $18 \rightarrow 16$ to match, the sequence becomes: 2, 3, 4, 6, 8, 12, 16, 24

When written this way, the sequence perfectly splits into two independent, alternating tracks where every single step just doubles the number from two slots prior ($a_n = 2 \times a_{n-2}$)

Even Positions doubles each time: 2 $\rightarrow$ 4 $\rightarrow$ 8 $\rightarrow$ 16

Odd Positions doubles each time: 3 $\rightarrow$ 6 $\rightarrow$ 12 $\rightarrow$ 24

By swapping that 9 out for an 8, you uncover a textbook example of an interleaved doubling sequence.