Big improvement looks pretty nice 

The way you're thinking about it currently-yes. Sinusoidal deformations occur in 3D rather than 2D, and the resulting effects on reflections do not resemble sine waves (due to their shapes being determined by the angles of incidence and therefore being only indirectly influenced by the wave motion), so it doesn't make much sense to draw them as such.

If you want to understand water in a mathematical way, then you'd need to work in 3D, as 2D necessarily obscures some important information. If you want to learn how to draw good-looking 2D water, then you shouldn't worry too much about the mathematics and focus on observing the effects, spend time looking at water (ideally, in real life so you can change your viewing angle, mess with the water surface, etc, but videos can be helpful too). Try animating some non-looping water from reference, at various angles and with various kinds of waves. You can always make it loop later once you have a better feel for how it works. Just as with walk cycles, billowing clothing, etc, IRL there aren't perfect loops for most natural things, but we animators always find a way to make it work by judging the details :]

Thank you for information...I really mean it.  Animating the water itself arent problem for me.. I would be happy if I can do the water animation without  2 pixel duplication movement.. This is the problem.Its really pain in ass animate when you need also duplicate 2 pixel  when you have like 8 different frames that also move.  So im  relieved that I was doing it wrong    .. I have done wave animation before but I never moved them like I did this time.

I did this very quickly..each side has just 1 frame so it does not look very solid.. but I wanted to test how the flow look with Three sides.. The reflection are also more thinner now.. I think it fits better.

This is good progress, the water has some more personality now.

I get what you're saying in reference to matching tiles to each other's 8 frame animation sequence. My advice with that is try and work in sub-divisions that can equally divide into the main tile. Eg; if you're scrolling something on a 16x16 tile, and the anim is 8 frames, then it'd make sense to scroll it in 2 pixel increments. That is the most basic way to think about it, but the logic can be applied in various ways to make life easier and the animations more controlled.

Of course a big part of animating tiles is going to be finessing the work: it's one thing to get a standalone anim to look good, but to get an animation to cooperate with other animations in varying scenarios is going to require some amount of work for each possible scenario. You can break the tasks down into smaller goals if that makes things feel more manageable.

Ty! I do the  2 pixel increments.. but what makes this harder is that my 8 frame itself have own movement animation.  If you combine those frames with 2 pixel increments.. Its very time consuming to fit together. .. The other problem is that when you make one side to match with another tile..  You need match both sides.. When you do that the tiles has basically new animation with slightly changes...Its like you have one tile with 16 frames and you need match them with another 16 frames for both side...Maybe its better if i dont animate each tiles.. or maybe I can mix them both like in my  previous edit?. . but my fear is that the water movement might look death... I will try to experimenting and find better method to make water animation look smooth without shit tons of work.

One relevant question is the ratio of your tiles, are they 1:1 or is there any foreshortening on the y axis due to the view (4:3, 2:1)? If so, I think you latter version is better because the side waves are shorter than width of the top waves. Even if the tiles are 1:1 the vertical shortening would be a good stylistic choice I think.

Also, are you going to put any classic watery texture on the surface, or going for plain color blue like Zelda with ocasional breaks? I wonder how a jrpg watery texture would interact with animated wavy borders like yours.

Thank you!

I made basic typical 16 bit water tile settings......I made very fast for  experimenting.. So I did not think about ratio.  I think the current  left side of shadow are way too wide.. I think it would look better with thinner size. Maybe that current wider shadow would fit if my intention was to make Zelda style perspective. The older version have less animation and its very wavey looking.. The new version might have too much bubble rounds.. So I might reduce it.

Yeah the water will look very simple like in Zelda. Its not going to have textures etc. I will put small light particle that will spam randomly in the water and maybe some water plants... I have never tried animating Typical Jrpg water.... So I dont know how it might work with the shadows..

It is a departure from what you have now, but in your examples I see that there are discrete globules of shadow separating periodically from the larger shadow/reflection. I wonder if you could integrate that element

Thank you.

Each tile has different animation movement.. So It might give that kinda of look... I did understand your point correctly?

I think you have the right ideas. Usually the sine-wave type movement of water happens on more axis than just one. In your latest example you've captured that movement on one plane of an axis, but there are two more axes to consider. By applying that same math to the other axes you can better recreate the undulating motions of water. In general all things animate along arcs in a cyclical fashion, so understanding that principal will illuminate its uses as a tool in many different scenarios of animation.

Nice to hear! I consider just  copypast the same tiles of left axis and add it to right side + change the right side  direction to down . So the loop flow looks natural... My issue right now is when I make new tile and combine it with another.. The flow does not match it 99% percent. So each tile needs a lot of adjustment... for example each tile has 8 frames and they need all match with another 8 frame tile. Its little bit hard to explain but I hope you understand.

I think it's very smart to research what you're trying to understand, and your attitude and approach are great! Looking forward to more progress, I think there could be a wealth of information for people to reference if you keep this thread active. Good luck!

Thank you. I will try to finish this. Its nice if this will help other people to learn..  I think solid  environments animations can improve the graphics a lot even if graphics arent best looking.