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Personally I find it useful to have some kind of theme or restriction. For example, if danmaku is being made for a specific character, what are that character's characteristics? What's their ability? Personality? Are they the kind of character that uses a certain type of danmaku? Are their attacks straightforward or tactical? etc etc etc.
Part of the reason why contests are popular is because contests with interesting restrictions force scripters to think creatively. Of course, trying to brute force ideas doesn't always work, but a large part of scripting patterns is taking basic components (rings, lines, etc) and transforming them into a pattern that works. A lot of the time designing patterns is not spent on implementing them but on tweaking them countless times so that they're just the way we want them.
Sometimes inspiration comes from daily life. Sometimes it comes from others. Take note of inspiration when it hits.
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A general note on pattern structure: A lot of attacks are combinations of constant attacks, phases, and the like. For example, you might have a constant stream of bullet rings accompanied by occasional bursts. Or perhaps the boss will switch between two patterns within the same attack such that the two patterns, when overlapping slightly, complement one another. A lot of it comes down to experimentation and seeing what combinations of sub patterns make the overarching pattern work.
Finally, in regards to experience. I'm experienced to the point where it's actually gotten difficult to think outside of the box - there's a growth phase for new scripters soon after they start where a lot of creativity comes through, and I'm long past it. You'll want experience playing these types of games and working with the engine so that you can unleash whatever creative potential you have, but beyond that experience doesn't help as much as being exposed to all kinds of potential ideas.
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