Weekly Problem: The Butterfly Numbers
A journey into emergence through binary patterns
Consider this sequence:
1, 3, 7, 15, …
Each number seems to follow a simple rule, but there’s something magical happening when we look at their binary representations. This sequence demonstrates how simple patterns create complex constraints – a fundamental concept in complex systems.
Try It Yourself:
Convert a number to binary to explore the pattern:
Think you’ve spotted the pattern? What’s special about:
- 1 = 1
- 3 = 11
- 7 = 111
- 15 = 1111
Count the number of 1’s in each binary number. How does this relate to the sequence?
The Challenge:
1. What are the next two numbers in the sequence?
2. Why does this pattern force each subsequent number to follow the rule?
3. How does this demonstrate downward causation?
Weekly Problem- Let’s get complex
