This experiment illustrates the theoretical core of the P System: the generation of numbers as symbolic structures.
Enter a limit to visualize the genealogy, symbolic representation,
and complete Morphogenetic Signature (φᴿ, φᴹ) of each number in the sequence.
Note: The limit is set to 1000 for the web version only.
What is the Morphogenetic Signature?
Each number generated by the P System possesses a "signature" that describes its structural properties.
- δ (Deltamorphism): Represents the total complexity of the structure, counting the total number of promoters (π) in its genealogy. A high value indicates a complex structure.
- ν (Variety): Indicates the number of unique promoters that compose the number. It measures the "width" of its genetic base.
- φᴿ (Relative Frequency): This is a feature of the extended signature. It is a list showing how many times each unique promoter appears (e.g., `[2, 1]` for the number 12, which is ⦅π₁↑2 ⊗ π₂⦆, indicates that π₁ appears 2 times and π₂ appears 1 time).
- φᴹ (Maximum Frequency): The highest value in the φᴿ list. It indicates which is the dominant promoter in the structure.
- ρ (Ramification): Calculated as (φᴹ - ν), it measures the genealogical "depth" relative to its "width". Positive values indicate strong dependence on few promoters.
- ω (Orbit): Corresponds to ν and represents the number of distinct genealogical "families" that contribute to the structure.
Results will appear here after generating the sequence.