Colorful Pattern Puzzle with Arrows and Warning Signs

Question

This is my first time on Puzzling Stack Exchange.

I challenge you to solve this puzzle I made, impossible to everyone else except for me as far as I know.

Can you solve it?

Answer 1

After rotating the each section so the numbers were oriented face up, each color, box, and arrow follows a strait-forward pattern.

The end product appears to be...

Let's label each grouping of 9 as boxes 1-9, with 1 being the upper left, the center top row being 2, the upper right being 3, etc. until the lower right box is 9.

Beginning with the numbers that start in box 4, the numbers follow the fibonacci sequence. The numbers starting in box 2 vary. The odd sets are sequential odd numbers. The even sets are a progression by one.

The box 1 coloration is a repeating pattern of red, blue, green, black. The box 2 is a repeating pattern of black, red, blue, green. The box 3 is a repeating pattern of green, black, red, blue. Note that boxes 1-3 are a rotation of the same color pattern.

Box 4 is an alternation of white or pink.

Box 5 is the rainbow, broken every 3rd color by light blue.

Box 6 is a rotation of colors purple, green, white, yellow, red.

Box 7 is a rotation of colors yellow, green, light blue, purple.

Box 8 is a rotation of colors red, purple, green, white, yellow.

Box 9 is a rotation of colors yellow, red, purple, green, white.

The arrow rotates clockwise and moves down a level upon full rotation.

The direction of the "no smoking" crossed-O is a pattern of right-right-left. The coloration seems to be a diagonal pattern of purple, orange, blue, yellow.

Answer 2

Here is a partial solve (I think?). I am stuck at the last couple steps and not 100% sure on a couple. Maybe someone can figure it out. Or maybe there is an overarching rule and these are coincidences.

The first thing to notice is that looking at the numbers, they are rotated in various directions.
In fact, from left to right, top to bottom, each square has been rotated clockwise in incrementing amounts. The second square is rotated once, the third square twice, and so on.
So the first thing to do is unrotate everything so that we can see what we have to work with:

Now some patterns become apparent: (labeling purple as violet, medium blue as indigo, light blue as blue, and dark blue as dk-blue; I wouldn't do this except OP hint was to think of a rainbow, so maybe it will become useful)

Numbers:

The numbers in the top row of each square are 3 2 5 3 7 4 9 5. This is: -1 +3 -2 +4 -3 +5 -4.
Next in the sequence is +6, so the missing number is 11. It goes in the top left (I think), as the position of the numbers in each column is MIDDLE MIDDLE LEFT. The numbers in the middle row are simply the sum of the prior 2 numbers. The next number is 21+34=55. It goes in the middle left like the rest.

Arrows:

The arrows are clearly rotating clockwise in incrementing amounts. So the missing arrow points to the left.
The position of the arrows in the bottom row are BOTTOM RIGHT, BOTTOM MIDDLE, ?. So maybe the final arrow goes in the BOTTOM LEFT, to finish the pattern.

Do not Enter: ("DOE")

Each DOE is in the center square. The orientations in the columns are \\\,///,\\?. So to complete the pattern, I assume we need \.
These are the colors used (sorted): VIOLET, VIOLET, ORANGE, ORANGE, YELLOW, YELLOW, DK-BLUE ?. My guess is next comes DK-BLUE so that each color is used twice.
Update: mkinson notes a diagonal color pattern of VIOLET ORANGE DK-BLUE YELLOW would support an answer of DK-BLUE. I'm not sure there are enough data points to know if that is the actual pattern but it is an interesting idea that gives weight to this guess)

Top row:

There is a clear pattern in the top row: RED BLACK GREEN DK-BLUE. In each square only 3 of the 4 appear (the 4th falls outside the square), and in each square the pattern shifts one to the right. So the missing top row is: RED BLACK GREEN

Middle left:

These are alternating WHITE PINK WHITE PINK... the missing square is WHITE

Middle:

We have BLUE RED ORANGE YELLOW BLUE GREEN INDIGO VIOLET ?. Or, BLUE + scrambled rainbow + ?. Update: Based on the OP's other puzzle, I think we need to use a six color spectral rainbow instead of a regular rainbow for the middle. So this would give us the six color spectral rainbow with light blue squares interrupting between each 3 colors. So the missing square's center would again be light blue (which I here refer to as BLUE). However, OP says center square has something to do with black. Maybe because the spectral colors can combine to form black?

Middle right:

We have VIOLET GREEN WHITE YELLOW RED, VIOLET GREEN WHITE ?. The next color in the pattern is YELLOW

Bottom left:

We have YELLOW GREEN BLUE VIOLET, YELLOW GREEN BLUE VIOLET, ?. The next color in the pattern is YELLOW

Bottom middle:

We have RED VIOLET GREEN WHITE YELLOW, RED VIOLET GREEN ?. The next color in the pattern is WHITE. This is the same pattern as middle right; perhaps this is important to solve the missing parts.

Bottom right:

We have the bottom middle pattern again, but shifted: YELLOW RED VIOLET GREEN WHITE, YELLOW RED VIOLET ?. The next color in the pattern is GREEN.

Mini-rectangles:
No idea. OP hint is something to do with black.