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Mathematics for Game Designers
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Recently updated threads
- Week 4: topics... Sat, 2011-02-19 17:32
- week 3: postings in the forum to check out Tue, 2011-02-15 04:08
- Games for Math designers Sat, 2011-02-12 22:49
- week 3: check-in and resources Wed, 2011-02-09 23:19
- week 2: examples Tue, 2011-02-08 02:13
about week 1
hello everybody,
i know that is probably late for a week 1 discussion, but i really need your help, I've used graphs before to solve problems, i have an idea about what they are and I'm familiar withs some algorithms that could be used on graphs, such as the shortest path algorithm, minimum spanning tree, hill climbing, simulated annealing and i guess breadth first search could also be used with graphs.
i want to know what material do you recommend to better understand graphs?
and when we talk about graphs for game designing,
r they used to represent the space of all possible states like in tic-tac-toe
|xoo|
|x x |
|o |
or r they used to connect objects like a map where each node represents a certain area?
They can be used in both the ways you mentioned, and perhaps a few more. Think about what a graph in essence is: it is a way of representing connections between things geometrically. So a game *board* can be a graph, a game *history* can be a graph, a *strategy* can be a graph. Wherever you have connections between things, abstractly speaking, you have graphs.
In any case, I think that your post sums up quite well the foundational understanding I was hoping people would achieve after week 1. Graphs will continue to come up in later weeks so feel free to continue to explore them!
If you find yourself becoming *bored* of graphs, you can always look into more complicated things... like these: http://en.wikipedia.org/wiki/Simplicial_complex
However for week 2 I suggest combining the idea of graphs with the idea of dynamics. Maybe a graph that dynamically grows? Or a graph whose connections dynamically shift? Or a graph in which "contents" move around?
As a game exercise, either find interpretations for existing games that have features like these - or invent some new games that do!
Let me be sure that I am on the same page with Joe here. For Board game ... one could use Depth First Search to have a sense of the direction to take.