I used some polynomials to make a nice, smooth terrain generator. Most people just use random numbers, I use random roots! For the people who do not know, a short summary about polynomials: A polynomial is an expression that contains one or more terms that CANNOT have either variables in denominators or variables in radicals. Some examples that are polynomials: 4x^3 (cubed) - 3x^2 +2x -1 7b + 10000b^2 a^2 Some examples that are NOT polynomials: 43/a + 3 √(a+ 52) - 2 √(2/a) The reason for these rules is so that NO MATTER WHAT THE VARIABLES ARE, THERE IS ALWAYS A VALUE. In division by a variable, there is no value when that variable is zero. In radicals, there is no (real) value when that variable is negative. Why I used polynomials I used polynomials because polynomials always have a value (as I said above). They also have the characteristic of being very smooth and never having drops, breaks, or sharp redirections (although it may look like it if you distort the scale enough). This means that my generator will generate land that follows those same rules.
