Type: XY - Bell curve
,exp(-(x²)),7,-2,2,2,0.5,100,-2,2,4,2,2,
Type: XY - Catenary
,cosh(x),7,-2,2,2,0.5,100,-4,4,8,4,2,
Type: XY - Cubic
,ax³+bx²-c,7,-2,2,2,0.5,100,-3,3,6,3,3,
Type: XY - Exponential
,be^x + ae^-x,5,-2,2,0.5,2,100,-2,2,6,3,3,
Type: XY - Hyperbolic
,ax + b/x,5,-2,2,0.5,2,100,-2,2,6,3,3,
Type: XY - Inverse quadratic
,1/(x² + a),5,-2,2,-2,2,100,-2,2,6,3,3,
Type: XY - Neile's semi-cubical parabola
,ax²^(1/3),5,0,2,2,0.5,100,-2,2,4,2,1,
Type: XY - Quadratic
,ax²+bx+c,7,-2,2,2,0.5,100,-3,3,6,3,3,
Type: XY - Quadratrix of Hippias
,x/tan x,7,-2,2,2,0.5,100,-10,10,20,10,10,
Type: XY - Sin(ax)/x
,sin(ax)/x,6,0,5,-2,2,100,-5,5,10,5,3,
When x = 0 both the numerator and the denominator of the expression are zero. Nevertheless the expression has a perfecly respectable value at that point - namely a.
Type: XY - Trigonometric
,a sin x + b cos x,5,-2,2,1,2,100,-2,2,12,3,6,
Type: Polar - Archimedean spiral
,θ^a,9,-1,3,-2,2,100,0,2,10,7,4,
Type: Polar - Cissoid of Diocles
,tan θ sin θ,1,0,3,-2,2,100,0,1.0,4,2,2,
Type: Polar - Cochleoid
,sin(θ) / θ,1,1.1,3,-2,2,100,-3.0,3.0,4,2,2,
Type: Polar - Conchoid
,1 + 1/cos θ,1,1.1,3,-2,2,100,-1,1,8,4,4,
Type: Polar - Double Folium
,4 (sin θ)² cos(aθ),5,1,2.0,-2,2,100,0,1,8,4,4,
Type: Polar - Fermat's spiral
,√(abs θ),1,1.1,3,-2,2,500,0,8,12,6,6,
Type: Polar - Folium of Descartes
,(3 sinθ cosθ)/((sinθ)³ + (cosθ)³),9,-1,3,-2,2,100,-0.5,0.5,6,3,3,
Type: Polar - hyperbolic spiral
,a/θ,5,1,5,-2,2,100,0,2,8,4,4,
Type: Polar - Kappa curve
,a/tan θ,5,1,5,-2,2,100,0,2,8,4,4,
Type: Polar - Lemniscate of Bernouilli
,√cos(aθ),1,2,5,-2,2,100,0,2,4,2,2,
Type: Polar - Limacon of Pascal
,b + 2a cos θ,4,-1,3,-2,2,100,0,2,12,6,6,
Type: Polar - Lituus (Bishop's crook curve)
,a/√θ,5,1,5,-2,2,100,0,2,8,4,4,
Type: Polar - Propellers
,(cos(aθ))²,4,0.5,2,-2,2,100,0,2,4,2,2,
Type: Polar - Rhodonea curves
,cos(aθ),3,1.0,3,-2,2,100,0,2,4,2,2,
Type: Polar - Right strophoid
,cos(aθ) / cos θ,3,1.0,3,-2,2,100,0,2,4,2,2,
Type: Polar - Trisectrix
,1 + a cosθ,5,1.0,2.5,-2,2,100,0.0,2.0,6,2,3,
Type: XY parametric - Archimedean spiral (parametric)
at cos(bt),at sin(bt),1,0.5,2,10,9,1000,0,5,6,3,3,
Type: XY parametric - Astroids
sgn cos t ×(abs cos t)^a,sgn sin t ×(abs sin t )^a,11,0,5,10,9,100,-3.3,3.3,4,2,2,
The sgn and abs convolutions are only necessary to complete all the quadrants.
The basic formula is simply:
          X  =  (cos t) ^ a
          Y  =  (sin t) ^ a
Type: XY parametric - Binet's formula
(c^t - cos(πt)×c^-t)/sqr5,(sin(πt)×c^-t)/sqr5,1,-10,10,-2,1.618,1000,-10,10,6,3,3,
This is the complex version of Binet's formula for the nth Fibonacci number:
    (p^n - (-p)^-n) / √5
where p is the golden ratio (1 + √5)/2
Type: XY parametric - Cycloid
t - a sin(t),1 - a cos(t),5,0,2,1,2,100,-5,5,10,5,5,
Consider a disc of unit radius rolling along a straight line. The cycloid is the locus of a point at a distance of a from the disc
Type: XY parametric - Ellipses
a  sin t,(4-a)cos t,7,0.0,3,-2,2,100,-3.3,3.3,8,4,4,
Type: XY parametric - Ellipses
a cos(t),sin(t),5,0.5,2,1,9,100,-3.2,3.2,6,3,3,
Type: XY parametric - Epicyclic curves
cos(t) + a cos(bt),sin(t) + ac sin(bt),1,0.333,0.8,3,1,300,-10,10,4,2,2,
a is the angle between the curve and the circle through the same point.
Type: XY parametric - Folium of Desctartes
3t/(1+t³),3t²/(1+t³),1,0.5,2,10,9,200,-5,5,6,3,3,
Type: XY parametric - Hyperbolae
a  / cost,(4-a)tan t,7,0.0,3,-2,2,100,-3.3,3.3,8,4,4,
Type: XY parametric - Iterative ellipse
x - y/b,y + x/c,1,0.5,2,50,100,1000,0,5,6,3,3,
Type: XY parametric - Lissajou's figures
2cos(bt + aπ),2sin t,5,0,1,2,2,100,-3.3,3.3,6,3,3,
b determines the ratio of the frequencies
a determines the phase difference at the start
Type: XY parametric - Nephroid
cos(t) + a cos(bt),sin(t) + a sin(bt),3,0.5,1.5,3.0,9,100,-3.2,3.2,6,3,3,
Type: XY parametric - Nicomedes conchoid
a tan(t) + sin(t),cos(t),5,-1.0,0.0,1,2,100,-1.6,1.6,4,2,2,
Type: XY parametric - Piriform
1 + cos(t),a sin(t) ( 1 + cos t),5,0.5,2,1,9,100,-3.2,3.2,6,3,3,
Type: XY parametric - Semi-cubic parabola
t³,at²,5,0.5,2,10,9,200,-5,5,6,3,3,
Type: XY parametric - Spirograph figures (Epicycloids)
(1 + a)cos(t) + ab cos(t(1 + a)/a),(1 + a)sin(t) + ab sin(t(1 + a)/a),9,-0.4,0.4,0.7,9,300,-10,10,4,2,2,
Sirograph figures are formed when a circle of radius a rolls round (inside or outside) a unit circle.

b is the distance of the penpoint from the centre of the moving circle (expressed as a fraction of the radius).
Type: Polar parametric - Infinity symbol
sin(at),cos t,2,1.0,2.0,-2,2,100,-3.2,3.2,4,2,2,
Type: Functional - A family of hyperbolae
,xy = ay² + 1,5,0.5,2,2,2,100,-5,5,10,5,5,
Type: Functional - Bicorn (cocked hat)
,(x² + 2ay - a)² = (a² - x²)y²,5,0.5,2,2,2,100,-3,3,6,3,3,
Type: Functional - Cubic ellipses
,ax³ + by³ = 8,5,0,2,1.00,2,100,-4.00,4,8,4,4,
Type: Functional - Cubic equations (type 1)
,x³ + bx² - ax = y,5,0,2,2,2,100,-5,5,10,5,5,
Type: Functional - Cubic equations (type 2)
,x³ + bx² - ax = y²,5,0,2,2,2,100,-5,5,10,5,5,
Type: Functional - Cubic equations (type 3)
,x²y + aby - a²x = 0,5,0,5,2.7,2,100,-5,5,10,5,5,
Type: Functional - Ellipses
,ax² + by² = 4,5,0.5,2,1.00,2,100,-3,3,6,3,3,
Type: Functional - Folium of Descartes
,x³ + y³ = 3xy,1,0.5,2,2,2,100,-3,3,6,3,3,
Type: Functional - Inclined ellipses
,x² + axy + by² = 1,5,0,1.5,1.0,2,100,-2,2,4,2,2,
Type: Functional - Lines
,ax + by = 1,5,0.5,2,1,2,100,-4,4,8,4,4,
Type: Functional - Pear-shaped quartic
,x³(a - x) = y²,5,1,3.0,2,2,100,0.2,3,6,2,3,
Type: Functional - Squircles
,x^a + y^a = 1,5,1,5,1,2,100,-4,4,8,4,4,
