Moderators: gmalivuk, Prelates, Moderators General
Dashboard Confessional wrote:I want to give you whatever you need. What is it you need? Is it within me?
What do you mean by this? Can't you just check the total XP against the triangular numbers like you would the Fibonacci numbers? Spreadsheets I've made for D&D 3 and 3.5 characters basically did just that, since those editions required 1000n points to move from level n to level n+1.King Author wrote:So do the Triangular Numbers, which I just recently learned about, but those ones you have to manually add together
gmalivuk wrote:What do you mean by this? Can't you just check the total XP against the triangular numbers like you would the Fibonacci numbers? Spreadsheets I've made for D&D 3 and 3.5 characters basically did just that, since those editions required 1000n points to move from level n to level n+1.King Author wrote:So do the Triangular Numbers, which I just recently learned about, but those ones you have to manually add together
gmalivuk wrote:It probably says that triangular numbers are stupid easy to compute, so do the math your own self, you lazy bum.
for(i=1; i<=1000; i++)
printf("%d\n", i*(i+1)/2);
Dashboard Confessional wrote:I want to give you whatever you need. What is it you need? Is it within me?
Snark wrote:I don't think it matters much whether you use Fibb or Triangular numbers for xp as long as your monsters xp is proportional to the same numbers.
Snark wrote:
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for(i=1; i<=1000; i++)
printf("%d\n", i*(i+1)/2);
There's your list you were looking for. Took me slightly less than 15 minutes. :)
f(x) = { 0; if x = 0, 1; if x = 1, 2 * f(x-1) - f(x-2) + 2; if x > 1
f(0),f(1),f(2),f(3),f(4),f(5),...
Thesh wrote:Favorite sequences of numbers?
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f(x) = { 0; if x = 0, 1; if x = 1, 2 * f(x-1) - f(x-2) + 2; if x > 1
f(0),f(1),f(2),f(3),f(4),f(5),...
MartianInvader wrote:You know that even if you reset to zero each time, you'll still level up much faster with triangular numbers, right? It's the difference between cubic and exponential growth, I believe.
It is in the limit, with the ratio of successive terms approaching the golden ratio.King Author wrote:I specifically avoided using the term "exponential" to describe Fibonacci 'cause I wasn't sure if it was technically correct.
nxcho wrote:My favorite sequence in the sense that it is the one I use the most is clearly the sequence of natural numbers (a_0 = 0, a_n = a_(n-1)+1). It is very useful for example counting things and it is easy to remember.
On the less trivial side of things I like sequences with a nice geometrical interpretation, like https://oeis.org/A089187
ElCarl wrote:Probably the fibonacci sequence...
So many interesting things about it :)
If you write down the sequence, then write down the differences between the numbers below it, you get the fibonacci sequence back out again!
And if you keep doing it to a long enough starting list, you begin to get the sequence coming out again on the left, except with alternating negatives and positive values.
i.e. you get:
...-21,13,-8,5,-3,2,-1,1,0,1,1,2,3,5,8,13,...
gmalivuk wrote:It is in the limit, with the ratio of successive terms approaching the golden ratio.King Author wrote:I specifically avoided using the term "exponential" to describe Fibonacci 'cause I wasn't sure if it was technically correct.
King Author wrote:Huh, never knew that. Neat. Did you know that if you use adjacent Fibonacci numbers in architecture, the result typically "looks" porportional and pleasing to the human eye? By "adjacent Fibonacci numbers" I mean if you want to build a rectangular room, if it's 13 meters lengthwise and 8 meters otherwise, for example. Of if you're building a step design, have the first be 3 feet, then 5, then 8, then 13, etc.
King Author wrote:I'm always wary of calling something "exponential" to simply mean "goes up a whole lot," because I do that sometimes in game design circles when talking about a given mechanic, and some mathy usually chews me out. "That's not exponential! It doesn't involve an exponent!"
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?