Various ores are placed down by COG in a variety of patterns. Some are very complex, others are simpler.
Limonite has three distributions that are each different based on which biome they spawn in.
Beach and RiverEditBeach and river limonite forms in small clusters of thin pockets, scattered around the water line. Fairly common, although due to the size and shape of beaches and rivers, it seems fairly rare. Occasional clay blocks are intersperced.
SwampEditSwamp limonite is a large pocket that ends to be below the water line, bit is a large, disperse, cloud over a wide area. Fairly common. Clay blocks and native blocks are commonly intersperced.
The jungle distribution is very similar to the swamp distribution, only it appears under ground.
IronEditIron is placed in a super-dense motherload, averaging about 30 blocks in diameter, with a haze of "hint veins" reaching out widely around it. Coming off the motherload are also extremely long narrow veins of iron ore which are very straight for the most part, although they do make quick changes in direction as they spread out across the landscape, although their height almost never changes. In this way, these tendrils can reach over a kilometer from the motherload.
The veins themselves are actually made up of four thicknesses of veing placement, the core being extremely small and only placing a handful of blocks, but made of of very dense ore. Each next larger vein places a thinner and thinner ore block until the outermost layer which is about 4 to 5 blocks in diamter and made up of the thinest of ores (metadata 1 or 2 nuggets).
GoldEditGold is placed in a very similar pattern as iron is, although it is more frequent in frozen biomes and farther down. There are some slight changes to the parameters on the veins, causing them to be straighter on average than iron, but otherwise identical.
DiamondEditDiamond ore is placed similarly to COG defaults, in pipes deep underground around a core of lava with the occasional monster egg scattered around for good measure.
RedstoneEditRedstone is placed in pipes, almost identically to a default COG install. More common in deserts. Due to being all over the place, expect to find flame lilies freaking everywhere. Flame Lilies spawn within 10 blocks of their distribution, compared to most other ores' 30 blocks.
TinEditTin is placed in very large clouds, with a knot of denser material towards the center. The largest volume is moderately populated by very low density ore blocks. Tin is most commonly found in plains, sunflower plains, forest, forest hills, and birch forest biomes.
CopperEditThe copper distribution is a very unique one. While similar to iron and gold in broad strokes, having the same veins that stretch out across the landscape, the motherload is made up of a number of vertically intersecting plates, similar to a desert rose crystal.
Many other mod ores use distributions identical to the original COG distribution with minor changes in frequency.