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A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

A curve obtained by fitting polynomials to each ordinate of an ordered sequence of points. The above plots show polynomial curves where the order of the fitting polynomial ...

The plane curve given by the equation axy = (a+x)(a-x)(2a-x) (1) = x^3-2ax^2-a^2x+2a^3, (2) which, solving for y, gives y=((a+x)(a-x)(2a-x))/(ax). (3) The plots above are for ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...