1.0
150
2.0
Amoeba (Gelfand-Kapranov-Zelevinsky 1994)
The amoeba A(f) = {(log|z|, log|w|) : f(z,w)=0} is the image of a complex curve under Log:(ℂ*)²→ℝ². Left: amoeba (sample points where |f| ≈ 0 along rays). Right: tropical curve = piecewise-linear spine — the limit as the Log map's base→∞. Tropical algebra: min replaces +, + replaces ×. The spine "balances" at each vertex (sum of edge directions = 0).
The amoeba A(f) = {(log|z|, log|w|) : f(z,w)=0} is the image of a complex curve under Log:(ℂ*)²→ℝ². Left: amoeba (sample points where |f| ≈ 0 along rays). Right: tropical curve = piecewise-linear spine — the limit as the Log map's base→∞. Tropical algebra: min replaces +, + replaces ×. The spine "balances" at each vertex (sum of edge directions = 0).