1: Create a new Image. 640480. You can take any size. Apply Filter / Render / Clouds / Plasma.

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2: Now do Filters / Distorts / Whirl and Pinch

Whirl angle: 130
Pinch amount: 1
Radius: 1

It should look like that now.

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3: Create a new transparent layer.

Use the gradient tool, use white as foreground color and black as background color. The fastest way to do this pressing D to reset colors and then X to swap the colors.

Form: Radial

Move the gradient from the center of the image to one of the four corners.

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4: Duplicate the layer. The original one name fade black. For this set the layer mode to Multiply.

The duplicate, which should be at the top, name light.

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5: Click the light layer.

- Colors / Brightness & Contrast, use values -65 / +45

Now apply Whirl and Pinch again. The values should be still saved from step 2, if not enter the same values. Only one value has to be changed: Pich from 1 to 0.8.

Apply the filter.

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6: Set the layer mode for the layer to Dodge. Duplicate the light layer to enhance the effect.

Activate the background-layer. Filter / Blur / Selective Gaussian Blur.

Radius: 50
Max. Delta: 70

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7: If you want a single color use Colors / Desaturate, then Colors / Colorize or Colors / Color balance like me if you want an icy version:

Shadows -30 / -30 / +30
Mids: -30 / +10 / 0
Highlights: 0 / 0 / 30

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8: Here is just an example i played with: a splash screen for gimp 2.4

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