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2025/08/31

UNNS Pattern Growth Simulator

UNNS Pattern Growth Simulator

Interactive exploration of mathematical patterns in f(M, N) = (M × N) + (M ÷ N) + (M - N) + (M + N)

f(5, 3) = (5 × 3) + (5 ÷ 3) + (5 - 3) + (5 + 3) = 26.667

Growth Pattern Visualization

UNNS Pattern
Integer Values
Linear Comparison

Sequence Analysis

Statistics:

Term Contribution Analysis

Shows how each mathematical term contributes to the final result

Asymmetry Demonstration

f(M, N) = f(5, 3)
26.667
f(N, M) = f(3, 5)
21.600
Difference: 5.067

UNNS is asymmetric: f(M,N) ≠ f(N,M)

Integer Pattern Predictor

Comparative Analysis

k UNNS Linear Quadratic Ratio

A comprehensive UNNS Pattern Growth Simulator that focuses on the genuine mathematical behaviors we've identified. Here's what it includes:

Core Features:

  • Interactive Parameter Control: Real-time sliders for M, N, and sequence length
  • Growth Pattern Visualization: Animated charts showing UNNS vs linear function comparison
  • Term Contribution Analysis: Visual breakdown of how each mathematical term contributes
  • Sequence Display: Live calculation of sequence values with integer highlighting

Mathematical Analysis Tools:

  • Asymmetry Demonstration: Shows f(M,N) ≠ f(N,M) with actual calculations
  • Integer Pattern Predictor: Explains when and why integers occur based on divisibility
  • Comparative Analysis Table: Side-by-side comparison with linear and quadratic functions
  • Statistical Summary: Real-time calculation of averages and integer frequencies

Educational Components:

  • Formula Breakdown: Shows step-by-step calculation with percentage contributions
  • Animation Mode: Automatically cycles through different parameter values
  • Visual Charts: SVG-based visualizations that update in real-time
  • Mathematical Insights: Explains the underlying mathematical principles

Key Insights the Simulator Reveals:

  • How the M×N term dominates for large values
  • Why integer values occur only when M is divisible by N
  • How asymmetry creates different patterns for f(M,N) vs f(N,M)
  • The relationship between growth rates and parameter choices

This simulator stays grounded in verifiable mathematics while providing an engaging way to explore UNNS patterns. It helps users understand the actual mathematical properties.

Try adjusting the sliders and using the animation feature to see how different parameter combinations create distinct growth patterns!

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