I'm very new to Inkscape. I've included a few screenshots to better explain what I'm trying to accomplish. 

Simply put - I'm trying to create patterns with colors on a rectangle grid and then apply a polar coordinates filter to have fun and experiment with the 360 degree element of it. 

I'm currently using GIMP and using the Filters -> Distorts -> Polar Coordinates to achieve this, though the raster pixels are kind of messy and I'm hoping there is a way to do this with Inkscape so I can clean up this technique and start making circular vector designs from the rectangle grid starting point.

Any input or direction is appreciated immensely! 

Thank you!

I'd try Path Effect->Bend:

Here's an example using groups and path effects. I drew everything inside a 45 degree quadrant and created a group. I used guides and snapping to align everything nicely.

[Path > Path Effects...] [Mirror symmetry] and use the node tool to move the reflection axis.
[Path > Path Effects...] [Rotate copies] [Number of copies: 4] and again use the node tool to adjust the axis.

Another method - Pattern along path 

@Polygon That is exactly what I want to accomplish! Thank you for taking the time to make that. I like the colors you used more. It looks way more sharp.

I spent 5 hours yesterday getting familiar with Inkscape. Took me an hour alone to figure out how to make my 45° angled grid.

Can someone help me figure out how to cut away part of the design? I attached a few screenshots.

I've wasted a few hours trying to do it using clipping, path difference, and slicing. It won't go away and I can't seem to figure out why. I've only managed to cover it with a white filled rectangle tool (see pic).

Any help is appreciated!

@Paddy_CAD That is an interesting way of making that design. I'll keep that in mind. Thank you!

@CelticOneDesign Love the celtic mandala art. Will check out the pattern along path feature. Thank you!

AlekhineSVG

Can someone help me figure out how to cut away part of the design? I attached a few screenshots.

I use shapes instead of strokes which lets you easy draw the design by snapping to the grid:

AlekhineSVG

"Can someone help me figure out how to cut away part of the design? I attached a few screenshots."

Just use Polygon's method to create the object, group everything,  then just copy the object as many times as needed to complete the "chain". 

Edit: LOL - I just figured out what you are trying to do. Sorry.

Another way is to convert the grouped object to a pattern, create a rectangle the same height but at a width you want, fill it with the pattern and use the pattern editor in v1.3.2 to adjust the result.

My method would be to create "terminal end pieces" for both ends like this example. Then simply repeat the chain pattern that Polygon created. 

BTW- Love that pattern!
 

Here's a variant combining tiling and Polygon's bend.

I spotted the symmetry in your design so I drew the initial shapes on a square grid and made a group. [Path > Path Effects...] [Tiling] with [Mirroring mode: ry+cx]. Draw a circle and copy it. Back to the tiles. [Path > Path Effects...] [Bend] [Link to path in clipboard].

The beauty of this is you can change the number of tiles and the size of the circle at any time.

@Polygon Thank you for making this visual GIF! This cleared it up. I spent some hours getting familiar with the node tool today.

@CelticOneDesign I'm going to experiment a little next project with your pattern editor method. Your Celtic knot patterns look very clean.

@Paddy_CAD I was able to replicate your Tiling - Mirror method and it made the process of doing this design idea so quick! I love the flexibility of having the option to add more tiles and adjust size of circle. Btw, the blue gradient with pink colors you used in your 7-pointed kaleidoscope SVG demonstration looks incredible!

Can someone help me figure out how to "unlink or unconnect" to the circle path? I have the size of the circle path set to where I want the object to appear and when I adjust the size of the object and release it, it "snaps" back to the circle path. The same thing happens if I simply try to move the object any where on the canvas. 

I've attached a screenshot of the object selected (it's where I'm currently stuck). Any input is appreciated! 

Select your shape then [Path > Object to Path]. This replaces all path effect calculations with the final coordinates.

Alternatively, in the Path Effects dialog, click the drop-down arrow right of the effect name. You can "flatten" a single path effect, leaving the others intact.

@Paddy_CAD That worked like a charm. Thank you!

So, I have one real final problem and question. I've included a few screenshot illustrations to better describe the problem I'm encountering.

The center points aren't coming together correctly and it's creating quite a mess at the midpoint. (see pic).

I'd like to make these designs with a closed center. In order to do this, the bottom points of the pattern will all need to converge at the polar origin point, at the same time. In other words, the bottom node points will all need to meet equally at the fixed center of the circle (see pic of grid).

I'm not sure if I'm doing something wrong or if I might need to try a different method. I tried leveling the bottom nodes of the pattern, I tried turning off Snapping, I tried changing the Grid - I'm at a complete loss of ideas how to correct this.

Any input or suggestion are sincerely appreciated!

There's a singularity here. As you get closer to the centre of the circle, the bend curvature increases to infinity at zero radius, and then goes negative. You're seeing round-off errors in the path effect calculations. I'm sure this occurs in Gimp too, but you just can't see it when the error is smaller than one pixel.

Open the group, select all shapes and switch to the node tool [n]. Select the nodes nearest the centre and use the keyboard shortcut [,] or [<] to shrink them together. If you overshoot use [alt+,] to apply smaller steps. This might improve the appearance but you'll always find a mess at some fractal zoom level.

@Paddy_CAD Thanks for clarifying this. I figured it was a round-off calculation error (not my error). I spent a few hours yesterday and today trying delete different nodes in the center but it made a worse mess. I think I'm going to try a different method.

I'm now encountering another issue (unrelated to the center issue). I included a couple screenshots to illustrate.

I want to try the design with white stroke lines crossed through it. I used the Pen tool to stroke white lines over the design (see pic), I then grouped it all together. 

This time when I select [Path > Path Effects...][Bend] a majority of the design disappears (see picture). This happens before I'm able to [Link to Path in Clipboard]. I'm not sure why [Bend] would do this.

Does anyone know why this might be occurring?

Any feedback or suggestions is appreciated!

I have no idea what's happened here. Perhaps you can upload the svg file.

@Paddy_CAD I attached the SVG file. I tried it new from scratch and this time it's not disappearing at [Path > Path Effects...][Bend], though it is "partially disappearing" at [Link to Path in Clipboard] to the copied circle path.

I appreciate any kind of help or suggestions on this. The only work around I can think of is to draw the white pen lines first and "paint bucket fill" in the colors? 

*EDIT: noticing now that it's not "disappearing" - more accurately the white lines are expanding, taking over the majority of the space. I made the white Pen strokes so thin - still at a loss why they would be doing this.

I actually had more success starting the design using the Pen Tool to draw white lines and using the Paint Bucket Tool to fill in the colors.

Though I'm now encountering a new issue. I felt this issue might possibly be easier to fix than the previous one. I attached a few screenshots to illustrate it.

The tiling mirrors are being 'divided/split' at their linking points - causing them to split when they Bend around the circle path (see pic).

Anyone know how to stop the 'divide/ split' from happening at the intersection of the [Tiling] - [Mirroring]. ? 

Any suggestions appreciated!

Mystery #15 solved. A straight line has no filled area, but when it's bent around a circle, each white line became a white-filled arc. Select the lines and set fill colour to none.

Mystery #16 solved. In the Path Effects dialog, use the "eyeball" icon to [Hide] the Bend and Tiling path effects. Your shape will revert to the original tile.

The tool controls bar reports the width and height of the selection. In this case [W: 24.011] and [H: 48] [mm]. That decimal in the width is the problem. At some point, the white grid and the coloured blocks were misaligned. The grid moved 0.011 mm left (or the blocks moved right).

[View > Display Mode > Outline] and zoom in as far as possible on the bottom left corner of the tile. This misalignment is undetectable at normal zoom levels but results in a tiny gap when you tile the group. I recommend microsurgery with the node tool or redraw the grid.

@Paddy_CAD Works like a charm now. Both issues are solved! I sincerely appreciate this.

I have one final question regarding the Pen - Stroke Paint Lines. I've included a few screenshots to illustrate the last problem I'm having.

Do you know how to shape the ends of the Pen stroke paint lines? (see pics)

I can only find one single node at the ends of the lines and I wasn't able to "add nodes" to the paint to pull and shape.

Any suggestions or input is greatly appreciated!

EDIT: I ended up selecting all the stroke paint lines and doing [Stroke to Path]. Spent some hours playing with it and it seems to do the trick. It did create some microsurgery splits at the mirror tile ends again, though, I seem to have fixed it.

EDIT 2: Now figuring out that [Stroke to Path] was unnecessary. [Join Selected Nodes] also works to join the pen stroke lines at their joints.