if you have pansies that came from hybrid island, they can make purple pansies. I believe this is true of any hybrids from hybrid island - they can make second generation colours that would be much harder to get the normal way. my pink and blue windflowers from hybrid island make rare purple windflowers all the time
anyways, if you don't have pansies as a native flower and therefor can't get them at hybrid island, what you need to do is:
first, plant two white pansy seeds (very important they are seeds so you know the genetics are correct) next to each other to make blue pansies
next, cross those blue pansies with red pansies from seeds (again, very important that they came from seeds)
any red pansies that come from that blue/red pairing will be special reds with genetics that can make purple pansies. dig them up and plant them somewhere separate so you don't get them mixed up. two special red pansies have a 6% chance of making purple pansies.
it's important to note that any red pansies that came from two special reds are NOT guaranteed to have the right genetics, so dig up any new reds they make and put them somewhere else or sell them.
When I saw that guide I figured special orange pansies no longer existed but before I got around to actually changing things the orange pansies got me a purple anyways. So I'm sure the special orange pansies still exist. I also heard of someone else getting purple pansies from just blue pansies.
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^yeah I'm not too familiar with the detailed mechanics of hybrid breeding in NL, but my understanding is that it's much more complicated in NH because in NH the flowers have actual proper genetics. because of that, you can get lots of different colours from the same combination depending on what genes the parent flowers have. the method I listed is just a way that definitely leads to purple pansies eventually, but there are other ways to get them
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I did some genetic calculations regarding getting higher % chance of getting purple.
The two special red can spawn two different genetic pattern for blue pansies. One of them is the same as blue that spawn from two seed whites. The other one has 25% chance of spawning purple. To figure out which one is the right one, breed blue with seed yellow to see if it will spawn orange pansy. The one that spawn orange is the blue that will spawn purple pansy.
I know it's more work to get a purple, but that's something to look into if you are not having any luck from two special red pansies.