TOPH
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COMPLEX MATH
COMPLEX ANALYSIS SUITE · TriPod LLC
10 TOOLS ·
JULIA · MANDELBROT · DOMAIN COLOR · CONTOUR · RESIDUE · RK4
SHA·
02880745b847317c...fcab763
256
ITER
1.0x
ZOOM
JULIA
ACTIVE
RESET
Z-PLANE
COMPLEX EXPLORER · DRAG TO MOVE
−
z = 0 + 0i
JULIA SET
f(z)=z²+c · LIVE RENDER
−
c =
+
i
dragon
spiral
galaxy
seahorse
MANDELBROT
SMOOTH COLOR · ZOOM/PAN
−
TOPH
FIRE
ICE
DOMAIN COLOR
arg→HUE · |f|→BRIGHTNESS
−
f(z)=
rational
mobius
cubic
sin
exp
RIEMANN SPHERE
STEREOGRAPHIC PROJECTION
−
SERIES
TAYLOR / LAURENT EXPANSION
−
FUNCTION
e^z = Σ zⁿ/n!
sin(z) = Σ (-1)ⁿz^(2n+1)/(2n+1)!
cos(z) = Σ (-1)ⁿz^(2n)/(2n)!
ln(1+z) = Σ (-1)^(n+1)zⁿ/n
1/sin(z) Laurent at z=0
drawPair: e^(iπz) TOPH
TERMS
N terms
8
COEFFICIENTS
CONVERGENCE RADIUS
R = ∞
CONTOUR ∮
DRAW PATH · NUMERICAL INTEGRATION
−
f(z)=
unit circle
rectangle
clear
∮f(z)dz =
draw a path...
RESIDUE
POLES · RES · RESIDUE THEOREM
−
SELECT FUNCTION
1/z — simple pole at 0
1/z² — double pole at 0
1/(z²+1) — poles at ±i
sin(z)/z³ — pole at 0 (order 2)
1/(z(z-1)) — poles at 0,1
e^z/z² — pole at 0
e^(iπz)/z — TOPH drawPair
POLES & RESIDUES
RESIDUE THEOREM VERIFICATION
COMPLEX ODE
z'=f(z) · RK4 PHASE PORTRAIT
−
iπz TOPH
z² attractor
z²-c
oscillator
AVAN
COMPLEX MATH ASSISTANT
CLR
−
API KEY
NOT SET
SAVE
CLR
CORTEX-LINK ACTIVE · AVAN READY · COMPLEX ANALYSIS MODE
residue thm
riemann ∞
domain color
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