Looking for a multivariate function with certain properties

In summary, the conversation is about a undergrad future scientist who enjoys programming in their free time to practice skills not included in their education program. They are currently working on a roguelike game with a focus on procedural generation, math systems, and AI. They are considering adding the ability to design or evolve creatures or weapons, with different parameters and a function to calculate effectiveness. The function could potentially involve adding or multiplying numbers, but the individual traits should also have synergy or be incompatible. The concept is visualized as a 3D function with multiple symmetrical hills representing efficient solutions. The conversation also touches on the possibility of using the Fibonacci sequence to create a landscape-like effect. The individual is unsure of the correct approach to finding a solution and
  • #1
Asteropaeus
143
36
As a undergrad future scientist, in my free time I like to do some programming to get some practice as my education programme doesn't include it, but it is a useful skill to have.

I am programming some type of roguelike game, so I can get away from graphics and focus on procedural generation, math systems, AI and stuff like that. It is never going to amount to anything but be entertainment and practice for myself.

So I am thinking about having the ability to design or evolve creatures or weapons. Some parts are going to be added together and the game is going to calculate the effectiveness.
So there are going to be some parameters. They can be the degrees of freedom. And a function is going to give the effectiveness given these parameters.

Now, the function can be to add or multiply the numbers and the higher the result, the better. But this is boring and one-dimensional. If traits or emergent properties are going to be combined, some should have synergy while others should be bad together.

When I imagine this as a 3d function with 2 independent variables, I can see a flat landscape with a number of round symmetrical hills. Ideally, all will be of slightly different sizes and heights. Every maxima of this hill is where the behavior the function describes is very efficient. Say, these represent two parts of say a weapon or a creature that are combined to give the final properties of the weapon/creature. The high values are going to be special rare solutions. Every part has one inherent value that is going to be one of the independent variables. All these maxima are going to be solutions the player would try to converge towards.

I have no idea how this function would look like algebraically. Maybe some silly combination of sinusoid functions. There must be some Fourier transform type of thing that can give a number of maxima in a certain domain.

Another thing I was thinking about is the Fibonacci sequence. If I take two random numbers and add them, the better these two numbers match a Fibonacci number, the higher the y value is. I can see how this can create a landscape like the one I described.

Am I on the right track? What would be the correct way to find a solution to a problem like this?

I guess a problem like this falls within the branch of analysis? Not sure so I posted this in general math. Feel free to move.
 
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  • #2
Ok, so I figured out I can use a sum different e^-(x^2+y^2).
 
  • #4
No. I think I am just looking at this in a way that's making it too complex.

I think I can just as well just use sinoid functions with different phases that have constructive or destructive interference. Then take a square and normalize it and see what the answer is.
 

FAQ: Looking for a multivariate function with certain properties

What is a multivariate function?

A multivariate function is a mathematical function that takes multiple input variables and produces a single output value. In other words, it is a function with more than one independent variable.

Why is it important to look for a multivariate function with certain properties?

Multivariate functions are useful in many fields of science, including statistics, economics, and engineering. By finding a multivariate function with specific properties, we can model complex systems and make predictions about their behavior.

What are some common properties of multivariate functions?

Some common properties of multivariate functions include linearity, symmetry, continuity, and differentiability. These properties help us understand the behavior of the function and make calculations easier.

How do you find a multivariate function with certain properties?

There are various mathematical techniques for finding multivariate functions with specific properties. One approach is to use optimization methods to minimize or maximize the function, subject to constraints. Another approach is to use regression analysis to fit a function to a set of data points.

Can multivariate functions have more than two variables?

Yes, multivariate functions can have any number of independent variables. In fact, some real-world problems may require multivariate functions with three or more variables to accurately model the system. These functions are often referred to as n-variate functions.

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