There are a few important points.
Temperature is very important. Hot air will rise very quickly, create what we call “thermals” – also known as updrafts. This hot air can then condense when its a lot higher than colder air. Hot air often also carries a lot of water, and so hot air water can produce towering clouds that seem to be “compacted”. Cold air forms low-sitting clouds that may be more stretched out as there is a bit more time to separate the water.
Pressure is very important. Low pressure can create “harder” (instead of fluffier) clouds which are more centralised and compact. High pressure can create very high-in-the-sky clouds which are fluffy/wispy.
“Wind” is related to pressure and temperature usually, but forgetting this, of course wind can move clouds around, potentially winds can separate large clouds into a few smaller clouds.
Of course, because wind, temperature, pressure and “the amount of water in the air” are related (they all affect each other), very generally we have a picture of 2 types of clouds – those which form on calm, sunny, high pressure days (high, spread out, white, fluffy/wispy, unlikely to rain). And those which form on windy, wet, low pressure days (lower, much more dense, often grey/black, occasionally with thunder).
There’s basically two types of cloud: stratus (flat) and cumulus (cauliflower).
Stratus form when the air is moist and stable. If a layer of the atmosphere has more water than it can hold, the water condenses to droplets within the layer. If they leave the layer, the slight difference in temperature or pressure is enough to evaporate them.
Cumulus forms when the atmosphere is moist and unstable. Heating from underneath causes a parcel of air to rise which, in turn causes it to expand and cool. This causes the water in the air to condense. If the air is very unstable, it can punch through the tropopause and into the upper level winds causing the distinctive shape of a thunderhead (cumulonimbus).
The regular lines and patterns are arrangements of those clouds. They form for several reasons. First, the atmosphere has waves like the ocean. so if a layer of cloud is almost right for stratus, the pattern of pressure changes from the waves can cause it to condense in the same regular pattern. Another reason is that the clouds self organize in certain ways. In a cumulus, the air around the outside of the cloud is descending while the air in the middle is rising (a circular convective cell). if another cell forms right beside it, the descending air from the two cells works together to reinforce the pattern. A fairly extreme example of this is a squall line where each cell actually starts the next one creating a line of thunderstorms, each more developed than the last.
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