Fuzzy Graphs Explorer
Revealing Mathematical Shadows Through Non-Binary Visualization
Transfer Function Based
50+ Equations
Real-time Rendering
💡 The Core Concept
Traditional graphing only shows where equations are exactly equal to zero. Fuzzy graphing reveals the entire mathematical landscape by visualizing the residual (how far from zero) at every point.
Intensity = 1 / (1 + α × |F(x, y)|)
Where α controls contrast and γ (gamma) adjusts brightness. Low residual → bright (near solution), high residual → dark (mathematical "shadows").
Binary Graph (Traditional)
Select an equation to begin
Solution (F ≈ 0)
No Solution
Fuzzy Graph (Non-Binary)
Select an equation to begin
Low Residual
Medium
High Residual
🎯 Key Features
Black Holes
Regions of infinite error where traditional graphs show nothing
Shadow Features
High-error patterns from division operations
Hidden Islands
Near-solutions that predict emerging features
Transfer Functions
Map residuals to intensity: I = 1/(1 + α|F|)
🎓 Mathematical Background
Transfer Function: The core of fuzzy graphing is the transfer function that maps residual magnitude to pixel intensity.
I = (1 / (1 + α × R))^(1/γ)
Where:
- R = |F(x, y)| - Absolute residual
- α - Contrast parameter (higher = more contrast)
- γ - Gamma correction (higher = brighter midtones)
- I - Output intensity [0, 1]