User:Sam Derbyshire/Gallery

Here is my gallery of mathematical pictures. If you have any ideas for something interesting to visualise, please say so on my talk page.

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Most of these images have been created with MuPAD, for which you can find some example code here, or with Mathematica, for which some relevant code is here.

My gallery

• Various 2D plots/animations
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  Second degree rational curve
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  Third degree rational curve
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  Fourth degree rational curve
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  Acnode
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  Crunode
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  Tacnode
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  Animation of hyperbolic functions
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  Swastika curve
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  Construction of a fifth order Bezier curve
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  Interpolation of Bezier curves
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  Van der Pol oscillator
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  Construction of a cobweb diagram
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  Cobweb diagram animation for the logistic map
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  Construction of an envelope of a family of curves
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  Construction of a roulette : Cissoid of Diocles
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  Construction of a roulette (variant)
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  Pedal curve of an ellipse
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  Pedal curve of a circle (limaçon)
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  Negative pedal curve of the limaçon (circle)
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  Evolute of an ellipse (astroid)
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  Evolute of a tractrix (catenary)
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  Involute of a catenary (tractrix)
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  Evolute of an epicycloid (epicycloid)
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  Involute of an epicycloid (epicycloid)
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  Contrapedal of an ellipse
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  Same curve : pedal of the evolute of the ellipse

• Epitrochoids and hypotrochoids
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  Limaçon
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  Cardioid
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  Nephroid
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  Limaçon
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  An hypotrochoid with a bigger inner circle : gives the same figure as an epitrochoid
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  Again : here, a nephroid
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  Deltoid
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  Astroid
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• Lambert W Function
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  Real part
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  Imaginary part
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  Absolute value
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  Combined

• Natural logarithm
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  Real part
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  Imaginary part
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  Absolute value
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  Combined

• Exponential function
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  Real part
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  Imaginary part
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  Absolute value
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  Combined

• Gamma function
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  Real part
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  Imaginary part
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  Absolute value
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  Absolute value small version

• Log of the Gamma function
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  Real part
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  Imaginary part
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  Absolute value

• Wright Omega function
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  Real part
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  Imaginary part
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  Absolute value

• Convergence and residues
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  Complex residues
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  Radius of convergence and Taylor series
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  Cosine function
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  Taylor approximation of the cosine function
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  Taylor cosine approximation (animation)
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  A graph explaining the values of x^y at (0,0)

• Tetration
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  Graph of ${}^{n}x$ for n > 1, showing convergence to ${\frac {W(-\ln(z))}{-\ln(z)}}$
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  Graph of $\left|{\frac {W(-\ln(z))}{-\ln(z)}}\right|$, showing ${}^{\infty }x$ in black

• Benford's law
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  Graph of the densities of the sets of natural numbers starting with different digits in base 10

• Young tableaux
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  Insertions for the Robinson–Schensted–Knuth algorithm
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  Result of carrying out insertions
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  Corresponding recording tableau
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  Another recording tableau
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  Row descent and Garnir elements
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  Straightening a tableau
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  Row descent and how to pick subsets for Garnir elements
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  Schur polynomials and the Lindström–Gessel–Viennot lemma
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  Animation of Viennot's geometric construction of Robinson-Schensted

• Coxeter complexes, etc
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  The Coxeter complex of a finite dihedral group
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  The Coxeter complex of the infinite dihedral group
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  The affine root system of type G2

• Affine Dynkin diagrams
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  A₀
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  A₁
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  A₂
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  A_n
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  D₄
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  D_n
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  E₆
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  E₇
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  E₈

• Kodaira—Néron classification
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  0 intersection matrix, case 1
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  0 intersection matrix, case 2
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  0 intersection matrix, case 3
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  A₁, case 1
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  A₁, case 2
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  A₂, case 1
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  A₂, case 2
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  A_n
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  D₄
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  D_n
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  E₆
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  E₇
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  E₈

• Morse theory
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  Contours around a saddle point
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  Flow lines on an upright torus
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  Flow lines on a tilted torus
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  Critical submanifold for the height function on a laid down torus

• Quadrics
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  Parabolic cylinder
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  Hyperbolic cylinder
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  Circular cone
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  Cone
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  Circular cylinder
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  Cylinder
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  Paraboloid
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  One-sheeted hyperboloid
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  Circular one-sheeted hyperboloid
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  Two-sheeted hyperboloid
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  Circular two-sheeted hyperboloid
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  Circular paraboloid
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  Hyperbolic paraboloid
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  Ellipsoid
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  Prolate spheroid
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  Oblate spheroid
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  Sphere

• Gaussian curvature
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  Oblate spheroid
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  Prolate spheroid
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  Gaussian curvature

• Commutative diagrams
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  A diagram depicting the homotopy lifting property of fibrations
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  Corresponding dual homotopy extension property of cofibrations

• Miscellaneous
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  A surface showing a global maximum
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  A surface showing a local minimum, only critical point, but not global minimum
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  A saddle point
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  The four-torsion of a complex torus
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  The Cantor set as the set of binary sequences
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  A stippled picture of a knotted torus (the knot 6_2)

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