Figure 4: Golden Ratio Performance Penalties (Cache Interference)
Window Size (bytes, log₂ scale)
Performance (ms/word)
512
1K
2K
4K
8K
16K
32K
64K
30
35
40
45
50
55
60
3×512
3×1024
3×2048
Fibonacci
Golden Ratio Analysis
Penalty performance: 57.0 ms
Baseline performance: 35.4 ms
Ratio = 57.0 / 35.4 = 1.61
φ = 1.618 (0.5% error)
Measured: φ = 1.608 ± 0.002
Cache Interference Penalties
(3 × 2^N windows misalign cache)
Fibonacci window
avoids penalty
Power-of-2 windows (optimal performance)
3×2^N windows (φ-ratio penalty, ~60% slower)
Fibonacci sequence (harmonic alignment)