Processing: Creative Coding and Computational Art

PROCESSING: CREATIVE CODING AND COMPUTATIONAL ART
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In multiplication, grouping doesn’t matter, so you don’t need parentheses in this case
either:
(a * b) * c = a * (b * c) = a * b * c
Non-associative property
Most of your expressions will be non-associative, and will therefore require grouping. In
the examples in the following list, notice how the placement of the parentheses changes
the value of the expression. (Remember, what’s between the parentheses is evaluated
first.) Please also note that the operator != means “does not equal.”
(a * b) + c != a * (b + c)
(4 * 5) + 6 = 26
4 * (5 + 6) = 44
4 * 5 + 6 = 26 (Multiply first, and then add)
(a – b) – c != a – (b – c)
(8 – 5) – 4 = –1
8 – (5 – 4) = 7
8 – 5 – 4 = –1 (Solved from left to right)
When in doubt, use parentheses to group; it can never hurt.
Distributive property
When multiplying an expression involving addition or subtraction (which is just addition of
a negative number) by another value, you need to multiply all the different elements in
the expression by the value, as the following three examples show:
4 * (a + b) = 4a + 4b
–(a + b) = –1(a + b) = –1a + –1b
6 * (a + b – c + d) = 6a + 6b – 6c + 6d
You can use the distributive property to multiply two binomials, as shown following:
(2x + 3) * (3x – 2)
= (2x * 3x) + (2x * –2) + (3 * 3x) + (3 * –2)
= 6x 2 + 5x – 6
This is a second-degree polynomial, or a quadratic equation.