﻿#1 Cubic
,ax³+bx²-c,7,-2,2,2,0.5,100,-3,3,6,3,3,
#1 Exponential
,be^x + ae^-x,5,-2,2,0.5,2,100,-2,2,6,3,3,
#1 Hyperbolae
,ax + b/x,5,-2,2,0.5,2,100,-2,2,6,3,3,
#1 Inverse quadratic
,1/(x² + a),5,-2,2,-2,2,100,-2,2,6,3,3,
#1 Quadratic
,ax²+bx+c,7,-2,2,2,0.5,100,-3,3,6,3,3,
#1 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.
#2 Archimedean spiral (polar)
,θ^a,9,-1.0,3.0,-2,2,100,-2,2,10,7,4,
#3 Archimedean spiral (parametric)
at cos(bt),at sin(bt),1,0.5,2,10,9,1000,0,5,6,3,3,
#3 Basket of ellipses
a cos t,(4-a)sin t,10,1.0,3.0,-2,2,100,-3.3,3.3,6,3,3,
#3 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
#3 Cycloids
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
#3 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.
#3 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
#Logarithmic spiral
cos(t) + a cos(bt),exp(aθ),1,0.1,0.3,3,1,300,-5,5.0,8,4,4,
a is the angle between the curve and the circle through the same point.
#3 Nicomedes conchoid
a tan(t) + sin(t),cos(t),5,-1.0,0.0,1,2,100,-1.6,1.6,4,2,2,
#3 Spirograph figures
(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 fugures 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).
#3 Squircles
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
#1 Trigonometric
,a sin x + b cos x,5,-2,2,1,2,100,-2,2,12,3,6,
#5-Ellipses
,ax² + by² = 4,5,0.5,2,2,2,100,-3,3,6,3,3,