Cluster ID
Unique identifier like "C25-D7-O3" for pattern grouping
Tools
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Deep AI
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chaos_fingerprint
chaos_fingerprint
$0.15 per callNumber DNA Clustering. Every number has a unique "DNA" based on its behavior in chaotic systems. Generate fingerprints using Collatz sequence lengths, digit roots, and omega function values.
Capabilities
chaos_fingerprint analyzes numbers through three chaotic lenses: the Collatz conjecture (3n+1 problem), digital roots (repeated digit sums), and the omega function (prime factor count). Together, these create a unique "DNA" fingerprint that clusters numbers with similar chaotic behavior.
Perfect for Collatz research, number classification, and educational visualization of chaotic systems.
Collatz Length
Steps to reach 1 in the 3n+1 sequence (e.g., 27 → 111 steps)
Digit Root
Repeated sum of digits until single digit (1234 → 1)
Omega Function
Count of distinct prime factors (30 = 2×3×5 → ω = 3)
Example
chaos_fingerprint
// Request
{"name": "chaos_fingerprint", "arguments": {"limit": 10000}}
// Response
{
"analyzed": 10000,
"clusters": {
"C25-D7-O3": [27, 54, 81, ...],
"C111-D1-O2": [27, ...]
},
"max_collatz": {"n": 6171, "length": 261},
"most_common_root": 9
}
Use Cases
Collatz Research
Find patterns in the 3n+1 problem by clustering numbers with similar trajectory lengths.
Number Classification
Group numbers by their "chaotic DNA" for pattern discovery.
Educational Visualization
Visualize how numbers behave differently in chaotic systems.