xx How far across, left or right. Positive is right of the middle, negative is left.x = 3 is a straight up and down line 3 squares right of the middle.
yy How far up or down. Positive is up, negative is down.y = 2 is a flat line 2 squares above the middle.
rr How far a point is from the middle.r = 5 is a circle with radius 5.
θθ (theta, or t) The angle around the middle, like the hand of a clock. One full turn is 2π, about 6.28.r = θ draws a spiral.
timetime Seconds since the picture started. Use it to make things move.y = sin(x − time) makes a wave that slides.
a b c k mSlider letters a, b, c, d, k, m, n, p, q, s, u, v and w are numbers you choose. Use one and a slider appears.y = mx + b gives you an m slider and a b slider.
ππ (pi) About 3.14. It’s how many times a circle’s width fits around its edge. Type pi or tap π.
ee About 2.718. A special number for things that grow or fade smoothly.e^(−r) fades out from the middle.
=Equals Both sides are the same. The computer draws every point where that’s true, making a line or curve.y = x + 1
<Less than The left side is smaller. Shades every point where that’s true. The open side of < faces the bigger number.y < 0 shades everything below the middle.
>Greater than The left side is bigger. Also shades an area.y > 0 shades everything above the middle.
<= >=Or equal Less than or equal, greater than or equal (≤ and ≥).
+ −Plus and minus Add and take away.
*Times Multiply. You can also just put things next to each other: 2x means 2 × x.3*x and 3x are the same.
/Divide Split into equal parts.x/2 is half of x.
^Power Multiply a number by itself. x^2 is x × x (x squared), x^3 is x × x × x.y = x^2 makes a U shaped curve.
( )Brackets Do this part first, or keep things together.(x + 1)^2 adds first, then squares.
| |Absolute value Throws away the minus sign, so the answer is never negative.|−4| = 4. y = |x| makes a V.
{ }Only here At the end of an equation, draws it only where the test inside is true.y = x {0 < x < 5} draws a short line.
,Comma Separates the numbers inside a function.mod(7, 3)
sin cosSine and cosine Wave makers. They go up and down between −1 and 1 forever.y = sin(x)
tanTangent A wave that shoots off to the top and bottom.
√ sqrtSquare root The number that times itself makes this one.sqrt(25) = 5
absAbsolute value Same as | |.abs(−3) = 3
expExponential e to a power. Grows faster and faster.exp(2) = e^2
ln logLogarithms The opposite of powers: how many times you multiply to reach a number.log(1000) = 3
floor ceil roundRounding Round down, round up, or round to the nearest whole number.floor(2.7) = 2
modRemainder What’s left over after dividing.mod(7, 3) = 1
min maxSmallest and biggest Picks the smallest or biggest of the numbers.max(2, 9) = 9
hypotDistance How far it is across and up together.hypot(3, 4) = 5
atanAngle atan(y, x) is the angle to the point (x, y).
fracFraction part Just the part after the decimal point.frac(2.75) = 0.75
signSign 1 if positive, −1 if negative, 0 if zero.
ifIf Color tab: if(test, yes, no) uses the yes number when the test is true and the no number when it isn’t.if(x > 0, 255, 0)
noiseNoise Color tab: a random-looking number from 0 to 1 for every point. Good for stars and sparkles.255(noise(x, y) > 0.99)
y = …Curve y worked out from x.y = x^2
x = …Sideways curve x worked out from y.x = y^2
r = …Polar θ spins around and r says how far out.r = cos(5θ)
x … yBoth sides x and y mixed together. Drawn where both sides match.x^2 + y^2 = 25