Spatial Weighting for Systematic Coverage

Design Logic Milestone - Hysteresis Project

2025-08-04

The Breakthrough

After persistent clustering behaviors that trapped our electromagnetic field explorers in repetitive corner-dwelling loops, we achieved systematic perimeter coverage through spatial weighting algorithms. The tentacles now demonstrate genuine territorial curiosity—avoiding their own histories while seeking uncharted electromagnetic territories.

Core Design Philosophy

Memory as Anti-Gravity: Instead of simple visit counting, each grid cell accumulates not just presence but proximity influence. Previously explored territories exert a kind of conceptual repulsion, creating invisible pressure fields that guide future exploration away from known spaces.

Distance-Weighted Desirability: The algorithm calculates attraction scores by considering not only virgin territory (zero visits) but the gravitational field of nearby visited areas. A pristine corner adjacent to heavily-documented regions scores lower than equally pristine territory isolated in unexplored quadrants.

Mathematical Aesthetics

float calculateDesirability(int gx, int gy) {
    // Virgin territory base attraction
    float baseScore = 1.0 / (visitGrid[gx][gy] + 1);
    
    // Proximity penalty from nearby exploration history
    float proximityPenalty = 0.0;
    for(int dx = -2; dx <= 2; dx++) {
        for(int dy = -2; dy <= 2; dy++) {
            // Distance-squared decay creates natural exploration gradients
            float distance = sqrt(dx*dx + dy*dy);
            if(distance > 0) {
                proximityPenalty += visitGrid[nx][ny] / (distance * distance);
            }
        }
    }
    
    return baseScore / (1.0 + proximityPenalty * 0.05);
}

Behavioral Emergence

Before: Neurotic corner-camping, 150+ visits to single grid cells, mechanical repetition After: Strategic territorial distribution, systematic quadrant exploration, organic coverage patterns

The system now exhibits what we might call cartographic consciousness—an awareness of its own exploration history that manifests as territorial avoidance behaviors. Each tentacle carries a mental map of where it has been, actively seeking the spaces between its memories.

Technical Tribulations

The 5×5 grid penalty radius creates natural exploration pressure gradients. Heavily-visited territories develop invisible force fields that deflect future targeting, while distant virgin areas accumulate attractive potential. The result: systematic coverage that feels organic rather than algorithmic.

Grid Memory Visualization:

(1,1:121/0.02) - Heavily documented corner, low desirability
(11,11:0/1.00) - Virgin territory, maximum attraction
(0,0:0/0.65) - Virgin but proximity-penalized by nearby activity

Artistic Implications

This breakthrough transforms repetitive robotic behavior into something approaching territorial intelligence. The tentacles now demonstrate what could be characterized as spatial memory, curiosity about the unknown, and even a form of aesthetic judgment about where to direct their attention.

The electromagnetic field mapping becomes not just systematic but thoughtful—each movement decision informed by accumulated spatial knowledge and an implicit drive toward comprehensive coverage rather than compulsive repetition.

Future Trajectories

With systematic coverage achieved, the next evolution involves dynamic exploration behaviors:

Gravity-influenced perimeter-to-center sweeps
Larger exploration radii (25° movement ranges)
Resistance dynamics against central gravitational pull
Multi-scale territorial awareness

The tentacles have learned to remember space. Now they must learn to move through it influenced by environmental coupling.

Implementation Status

✅ Milestone Achieved: Spatial memory prevents clustering ✅ Systematic Coverage: All perimeter regions targeted sequentially
✅ Distance Weighting: Proximity penalties drive exploration outward 🔄 Next Phase: Gravity-influenced movement dynamics and broader exploration patterns

This represents a foundational breakthrough in autonomous territorial exploration behavior for electromagnetic field mapping installations.