Sandpile SOC — BTW Model
Bak-Tang-Wiesenfeld · Avalanche Statistics · Power Law · Self-Organized Criticality
BTW Sandpile
Grid size N
40
Critical height z_c
4
Grains per batch
1
Reset Grid
Add Grain(s)
Auto Run
Stop
Grains added:
0
Total avalanches:
0
Last avalanche size:
0
Max avalanche:
0
BTW Rule:
Drop grain at random site (i,j):
z(i,j) += 1
If
z(i,j) ≥ z_c
, topple:
z(i,j) -= 4
z(neighbors) += 1
(boundary: grains leave system)
Avalanche size distribution:
P(s) ~ s^(-τ)
, τ ≈ 1.0 (2D BTW)
SOC:
System self-tunes to critical
state — no fine-tuning needed
Color:
black=0, yellow=z_c-1