Gaussian Alpha on texture

I’m trying to render fire using texture splats, and the article I’m reading suggests a gaussian function for the alpha on the texture, i.e., alpha turns to transparent gradually as you move away from the center of the texture. I’m pretty new at this so I’m not even sure where to begin. I built a function that can give me a matrix NxN where N is the size and it takes in a standard deviation and gives me back a 2d gaussian map, normalized so I can use it for alpha, but I’m not quite sure where to go from there. Do I need to turn this matrix into an array of bytes representing alpha and somehow replace the cooresponding bytes in my texture image or what? Thanks!