As you see i have 3 tutorials in GIMP my photoshop will come in a few hours/days.
Here's our odd outcome:
File > New, as usual. Bucket fill the background with a darkish colour that isn't black. I'm using a shade of purple here (6d2051).
Create a new layer and bucket fill it with black. Now get out the gradient tool and set the options as follows:
Now drag out a few gradients on this layer. Only do a handful and drag the mouse out a fair bit on each one. We're aiming for something like this:
I'm calling this layer "Grad Diff 1" for reference purposes, as we'll need it later. Duplicate this layer. Set the original layer's mode to Overlay.
Go to the copied layer (which I will be calling "Grad Diff 2" for reference purposes). Start dragging out more gradients on this layer. Do quite a few and include some shorter drags of the tool this time. We want this layer to be a bit more chaotic, like this:
Hide that layer now. Make a new layer called "Circles". Now we're going to use the paintbrush tool to paint some hard round circles on this layer to form the basis of our design. The Scale Brush option of 2.4 or a custom resizable vbr brush in either Gimp version would be ideal here, as we don't want the circles to be all the same size. My design involves starting in the bottom-middle and working up in a diagonal direction, with the circles going smaller as we go up. Add about 3-4 circles in this way. Note that the colour you paint with on this doesn't matter.
Duplicate Grad Diff 2 layer and show the copy and hide the Circles layer. Alpha to selection the circles layer (right-click the layer in the Layer Dialog and select the option), switch to the copied Grad Diff layer, invert selection (Select > Invert) and delete selection (Edit > Clear). Deselect all (Select > None).
Make a new layer called "Lines" and then pick the Path tool. Place the first anchor just below the lowest circle off the canvas and then place the second anchor above the canvas at a diagonal angle going in the flow of the circles. Click the "Stroke Path" button on the tool options. Set the line width to 10 and OK it. Now move the 2nd anchor over so far to the right (up to you how far) and stroke path again with the same settings. Again, colour doesn't matter here.
Reshow the Grad Diff 2 layer and make sure it is positioned below the gradient circles. Go to Layers > Transform > Rotate 180. Alpha to selection the Lines layer, switch to the Grad Diff 2 layer, invert and delete selection. Deselect all.
Copy the "Grad Diff 1" layer and make sure the copy is positioned below the gradient shape layers. Change the layer mode to addition and erase around the shapes with a soft eraser.
Copy this layer and move it to the top. Change the layer mode to Overlay. Now go to the Layers Dialog and click the checkbox there to maintain transparency. Now bucket fill this layer with white.
Copy visible and paste as new layer. Go to Filters > Map > Paper Tile. I used the follow settings (you may have to adjust them slightly, but the division x and y values should be the same regardless):
Set the layer to Lighten Only.
Copy visible and paste as 2 new layers. On one layer go to Filters > Artistic > Cubism. Set the tile size to 20 and OK it.
Hide this layer. On the other layer go to Filters > Map > Displace. Set the dropdowns to the Cubism layer we just made. Set the On Edges to Smear. If using 2.4, make sure the displacement type is Cartesian. Now mess around with the x and y values so the displacement flows with the design. Like, my design goes towards the right-corner, so I'll use displacement settings that flow that way too.
Copy visible and paste as 2 new layers. On one go to Filters > Artistic > GIMPressionist. Select the Ballpark preset. Click apply and then OK it.
Hide this layer. On the other layer go to Filters > Map > Displace. Change both dropdowns to the ballpark layer and leave all others settings as they are. OK this and set the layer mode to Lighten Only.
Copy visible and paste as new layer. Go to Filters > Edge Detect > Edge. I used the default settings here but feel free to mess around with the settings. OK it and set the layer mode to Overlay.
Create a new transparent layer. Paint a white blob over the biggest circle (effectively the "start point" of the abstract). Blur it by a high amount (I used 150) and set it to Grain Merge. Alter opacity if it comes out too bright.
Copy visible and paste as 2 new layers. On the lower layer go to Filters > Blur > Gaussian Blur and use a really low amount (I used 1) and OK it.
On the other layer go to Filters > Enhance > Sharpen. Choose an amount that looks appropriate (I used 30) and OK it. Free select the abstract, feather the selection (Select > Feaher) by a good amount (I used 40), invert and delete selection. Deselect all.
Copy visible and paste as new layer. Go to your Gradients Dialog and make sure the "Default" gradient is selected. Go to either Filters > Colours > Map > Gradient Map (2.2) or Colours > Map > Gradient Map (2.3 or 2.4). Free select around the abstract and feather it by a high amount (I used 100). Delete selection, then deselect all. Lower opacity to suit (I lowered it to 50). Then add a border and you're done.