I'll keep it short. There are, at least to me, two prevailing patterns. Altcoins in general, across the board move in tandem with Bitcoin's fortunes. It's no coincidence that 2017 saw the crypto "boom", all this fueled by Bitcoin's rising prominence. Also no coincidence that alt all time highs coincided in the same period that Bitcoin did.
There are also periods where alts do well while Bitcoin moves sideways, but this is only the alts recovering or gaining back ground while Bitcoin consolidates. This is only after they wither during Bitcoin's downturn. When BTC falls, alts fall harder. When BTC recovers, alts recover quicker.
Yep, overall there's positive correlation. In a short term period all sorts of weird and whacky stuff happens. There are even periods where alts fall because BTC is rising, that's when people panic sell their alts to get their money in to bitcoin.