Complex Function Viewer (Conformal Maps) play online

Enter any equation of variable z and produce a complex function graph (conformal map) generated with domain coloring right on your device!

Notable features include:
Extensive and easy-to-use touch interface.
Over 50 mathematical functions, including special functions like gamma, iterated functions, lambert-W, and Riemann-zeta.
Images on the complex plane (conformal mapping of images).
Contour integration (drag a path), derivatives, and function values.
Save, load, export, and import your favorite equations.
Save images, view your saved images, and later load the specific equation and bounds back into the app for more exploration.
Many customizable settings.
A tutorial to familiarize you with the app and example equations.
Complete documentation within the app available through the "about" menu.
Easily give feedback.
Useful for complex analysis.

Supported math functions and constants:
(u and v represent arbitrary functions of z)
Arithmetic:
Addition: u + v
Subtraction: u - v
Multiplication: u*v
Division: u/v
Negation: -u
Exponentials/logarithms:
Exponentiation: u^v or u**v or pow(u, v)
Square root: sqrt(u) or (u)
Natural exponentiation (of base e): exp(u)
Natural logarithm (of base e): ln(u) or log(u)
Branched natural logarithm (of base e): ln(u, branch)
Based logarithm: log(u, base)
Branched and based logarithm: log(u, base, branch)
Lambert-W function: W(u) or lambertW(u)
Branched Lambert-W: W(u, branch) or lambertW(u, branch)
Super square root (inverse of u^u): ssqrt(u)
Trigonometric functions:
Sine: sin(u)
Cosine: cos(u)
Tangent: tan(u)
Cosecant: csc(u)
Secant: sec(u)
Cotangent: cot(u)
Inverse trigonometric functions:
Inverse sine: asin(u)
Inverse cosine: acos(u)
Inverse tangent: atan(u)
Inverse cosecant: acsc(u)
Inverse secant: asec(u)
Inverse cotangent: acot(u)
Hyperbolic trig functions:
Hyperbolic sine: sinh(u)
Hyperbolic cosine: cosh(u)
Hyperbolic tangent: tanh(u)
Hyperbolic cosecant: csch(u)
Hyperbolic secant: sech(u)
Hyperbolic cotangent: coth(u)
Inverse hyperbolic trig functions:
Inverse hyperbolic sine: asinh(u)
Inverse hyperbolic cosine: acosh(u)
Inverse hyperbolic tangent: atanh(u)
Inverse hyperbolic cosecant: acsch(u)
Inverse hyperbolic secant: asech(u)
Inverse hyperbolic cotangent: acoth(u)
Special functions:
Lambert-W function: W(u) or lambertW(u)
Branched Lambert-W: W(u, branch) or lambertW(u, branch)
Super square root (inverse of u^u): ssqrt(u)
Gamma function: gamma(u) or (u)
Factorial function: u!
Binomial function: bin(u, v) or binomial(u, v)
Error function (coming soon): erf(u)
Riemann-zeta function: zeta(u)
Riemann-xi function: xi(u)
Comparisons:
Equal: u == v
Not equal: u != v
Less: u < v
Greater: u > v
Less or equal: u <= v
Greater or equal: u >= v
Logical operators:
And: u & v
Or: u | v
Not: ~u
Auxiliary functions:
Absolute value: abs(u)
Complex argument: arg(u)
Real part: x or re(u)
Imaginary part: y or im(u)
Complex conjugate: conj(u)
Ceiling: ceil(u)
Floor: floor(u)
Minimum: min(u, v)
Maximum: max(u, v)
Random functions:
Random number in range: rand(min, max)
Constants:
Imaginary unit: i or j = sqrt(-1)
Euler's Number: e = 2.718281828
Pi: pi or = 3.1415926535
Golden ratio: phi = (1 + sqrt(5))/2 = 1.6180339887
Branch functions:
If statement
If-else statment
Definitions:
Define your own variables
Redefine your own variables
Iterated functions:
Iterated function
Summation
Product