How is the playing schedule created for tournaments where the teams are seeded?

For example, a tennis or basketball tournament, where the tennis players and basketball teams have a relative ranking. The idea is to set things up so the top two seeds cannot face each other until the finals, none of the top 4 seeds can face each other until the semi-finals, none of the top 8 seeds can face each other in the third to last round, and so on. I did a google search and all I found were bracket charts that you could download.

I came up with a straightforward way of doing this. It takes a bit of repetitive effort, but can easily be programmed into a computer. There is of course more than one way of satisfying the requirements.

Can you come up with a method? Your answer would be represented by a bracket chart. All the seed numbers are written in a line. In the first round, the first two seeds play against each other, as do the second two and so on. In a similar way, winners of consecutive games play against each other in the next round of the tournament.