Symmetry puzzles are really hard to grasp

[outlaw_hat]

I'm having a really hard time understanding how they work.

Any tips?

[N-dorfyn]

first (re)read the tips for symmetry puzzles in the encyclopedia

these are going to sound silly, however:
for the Lotuses, tilt your head to match the line of symmetry you are working on.
for the galaxies, put you finger on the screen and count squares

[MannyKlystron]

Could also run through the Pillars of Insight a second time.
It's the viewpoint clues that give me a headache.

[Osmium]

I also struggled with these at first, especially the rotational symmetry.

Linear symmetry, the lotus ones, just comes down to making sure the left side mirrors the right side. If the lotus is white and you know the square immediately to the right can't be white, than neither can the square to the left. You basically retrace the path from one side onto the other side. If the lotus symbol is pointed diagonally, you can tilt your head in that direction so it looks up and down to you again and apply the same logic.

The galaxy symbols are rotational symmetry and are a little trickier. The pattern needs to fit in the same space in the puzzle even if you rotate it 180 degrees. You don't need to turn your screen upside down to do it or anything, though. If the path through the center of the symbol goes left two squares and up one, then you know the right side goes right two squares and then down one. Any direction changes that happen on one side are reversed on the other. The main difference between this and linear symmetry is that this reverses up and down while linear doesn't. Linear also needs to point in a direction to tell you which axis you're reflecting across, but rotational doesn't.

This is linear symmetry:




The blue arrow is a white lotus symbol arranged vertically

This is rotational symmetry:





Notice how any step outward from the center in any direction needs to be done on the opposite side. Any change in direction also needs to be flipped and done to the opposite side.
You tend to get more spiral patterns, which is why they go with the galaxy symbol for this type. It's possible for an area to have both linear and rotational symmetry and those tend to have more regular patterns.

[outlaw_hat]

Thank you for the tips! Though I haven't reached the galaxy ones, I don't have a problem with simple symmetry. It's when there are multiple lotuses and the symmetry breaks (to me) in a weird way.

Originally posted by Osmium:

If the lotus is white and you know the square immediately to the right can't be white, than neither can the square to the left.

What? Really? I must have missed that!

[Osmium]

With multiple lotuses you need to figure out if their regions can touch. Two vertical lotuses can never be part of the same area unless they're aligned vertically. If they were side by side, any attempt to balance one would unbalance the other. If they're facing different directions, then you need to see if there's enough room in the puzzle to satisfy both axes of symmetry. If completing the pattern with both lotuses together would take you past the edge of the puzzle, then you know those lotuses must be separated by a band of the opposite color.

If one area has like 5 lotuses pointed in different directions, then that pattern is very constrained. It can't get too crazy with branches unless there's room for a copy of that branch on the other side of the reflection point of every lotus.

For example, a 7x7 grid that's entirely white squares with black squares in each corner has a TON of symmetry. You can flip that horizontally, vertically, diagonally, and even rotationally. If you replace a single black square with a white one, almost every line of symmetry is broken. Any shape with multiple symmetries has to have a lot of repetition in it and knowing even a corner of it tells you the rest.

[Shiyuro]

I'm having a hard time too, sometimes it doesn't feel symmetrical at all (for me too).
The fact that when you add other rules to it, it just break the symmetry everywhere making it even harder to comprehend.