Disagree about symmetry, it's boring. It's also not very dwarfy. Dwarfs are not logical and they do not plan things. I follow ore veins and fit rooms off of those.
I disagree about dwarves not planning things. My dwarves always tend to build highly symmetrical and modular forts. Completing a pre-planned structure never comes second to mining out a valuable vein or a cluster. They have a strict set of rules and safety regulations to follow when carving their mountainhome. That's just how they like to do things. And why it takes a dreadful amout of real time to get just a few things done in the simulation.
On the actual topic, mineshafts, there are also standardized solutions my dwarves use. To best understand the patterns of their exploratory mining shafts, their motives need to be explained first. After bureaucracy, they hold the metal industry in the highest esteem – even higher than the elf/goblin bone industry. When mining, they only look for veins of metal. Any kind will do, for the industry must be both running at 100% and growing as fast as possible.
To find veins, my miners mainly dig in grids, leaving behind untouched areas of 11-by-11 blocks. This falls between the
7-by-7-block and 15-by-15-block designs presented in the Wiki. Why do they use a grid and why is it 11-by-11? The answer lies in the principles stated above: A grid of that size finds most of the worthwhile veins and looks organized. Also, the gridsize is standard in the whole fortress for all rooms of the same purpose, tombs.
Those 11-by-11 blocks not mined through for metal ores will be carved into designated 7-by-7 tombs for every laydwarf in the fortress. For them, there is no place more honorable to be buried than in the very heart of what they sacrificed their entire lives for.