Hypercomplex stuff

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Navigation

Functions of a hypercomplex variable

Structures

Number systems

Shapes

Special constants

Sets of functions

Functions of functions

Generalized Mandelbrot sets and Julia sets

Generalized Cauchy-Riemann equations

Full page

Recreational monocosm

WIP

thingy about multidimensional numbers or something

Complex map of \(\zeta (\frac{1}{2} + {\acute {i}} t)\) where \(t \in [0, 75]\).

Complex \({\rm {cheta}} (z)\) domain colouring.

3D plot of \({\color{#2D70B3} \vert}\)\(\Gamma (z)\)\({\color{#2D70B3} \vert}\) over the complex numbers (animated GIF)

Navigation

• Multiplication
• Spacetime globes
  • Classical and special relativity
  • Penrose diagrams (split-complex maps / contour plots)
• Generalized polygons
• Stereographic projection of a sphere
  • Stereographic projection of Earth's night sky
  • Stereographic projection, regular polygons and regular polyhedra as spherical tilings
  • Spherical tilings as meromorphic functions
• Euclidean plane
  • Euclidean tilings as meromorphic functions
• Poincaré disc and half-plane models of the hyperbolic plane
  • Hyperbolic tilings in the Poincaré disc and half-plane
  • Hyperbolic tilings as meromorphic functions
• Map projections of Earth
  • Equirectangular projections (plate carrée, Cassini projection)
  • Transverse Mercator projection (complex maps / contour plots)
  • Littrow projection (complex maps / contour plots)
• Elliptic curves (portal)
  • Weierstrass elliptic function('s derivative)
• Tetration (portal)
  • Pentation
• Solar System
• Colourimetric functions
  • Chromaticity diagrams
  • Spectral power distribution to colour calculators
• Planck's law
• Stellar temperature colours
• Stellar evolution
• Stellar class percent fractions
  • Zero age main-sequence star cluster generators
• Relativistic Doppler shifting
• Star size from luminosity and temperature
• Taxicab geometry
• Chebyshev geometry
• Gamma function
• Factorials (portal)
• Zeta function (zeros / Lehmer pairs)
• Prime counting function
• Fourier transforms
• Mandelbrot set
• Julia sets
• Recreational monocosm

Functions of a hypercomplex variable

Arithmetic

Hypercomplex components

Polynomials, Rationals, Exponentials, and Logarithms (Part 1)

Polynomials, Rationals, Exponentials, and Logarithms (Part 2)

Trigonometric functions and inverses

Hyperbolic functions and inverses

Sinc analogues

Logistic functions, Gudermannian, and inverses

Algebraic curves

Bessel-type functions

Integer functions

Factorials and binomial coefficient

Productlogarithms, hyperoperators, and relatives (Part 1)

Productlogarithms, hyperoperators, and relatives (Part 2)

Physical functions

Lp trigonometric functions

Exponential integral and relatives

Elliptic integrals, elliptic functions, and relatives (Part 1)

Elliptic integrals, elliptic functions, and relatives (Part 2)

Elliptic integrals, elliptic functions, and relatives (Part 3)

Gamma functions and relatives

Error functions and relatives

Zeta functions, Polylogarithms, and relatives

Modular forms and relatives

Generalized Mandelbrot sets and Julia sets

Posts (in ideal reading order)

• Part I: Cursory overview of familiar territory
  • Visualizing complex functions
• Part II: Split-complex and Dual numbers
• The Family
• Residues of Singularities
• Extremely multivalued functions
• Tetration Portal
• Factorial Portal
• Hypernomials
• Zeros of the Riemann zeta function
• Function list (alphabetical)
• Special function evaluations and approximations used
• Polygon formula tables
• Pseudogons, Complexgons, and more
  • Schläflians of polytopes
  • Generalized Cartan matrices of complex polytopes
  • Apeirogons
• Astronomy Portal
• Stellar evolution
• Stellar class percent fractions