Amplitwist: Local Shape under Complex Maps
From Tristan Needham's Visual Complex Analysis, Chapter 4 (A Puzzling Phenomenon — the Amplitwist concept). A local patch of the domain is mapped by w = a·z (analytic) or w = a·z + b·z̄ (general). An analytic map turns the unit disk into a circle (a pure amplitwist); a smooth general map shears it into an ellipse. Adjust the stretch (amplitude |a|) and twist (rotation θ) with the sliders or pick a preset. Space toggles, R resets.
Key insight
An analytic map preserves circles (Amplitwist). A smooth non-analytic map deforms a small disk into an ellipse.
Amplification1.5×
Rotation30°
Presets
Image Shape · Circle (r=1.50)
Major Axis · 1.50
Minor Axis · 1.50
Status · Stopped