To get a usable size to apply on the tools used, I am going to use a factor “x”. x can easily be calculated on an image with a 4:3 aspect by
just taking 1% of the longer side of the image. E.g. if your image has a size of 800*600 pixels, x would have a value of 8.

First, we are going to slightly adjust brightness and contrast be 10% “Colors” → “Brightness / Contrast”
Brightness: +10%
Contrast: + 10%

Now let’s make the colors a bit more intense
“Filter” → “Increase” → “Unsharp Mask”

Radius: 1x
Amount: 1
Threshhold: 0

In order to get the best possible effect on the image, we’re going to reduce the amount of colors

“Colors” → “Posterize”: Colors: 3 or 4 (prior to GIMP 2.8: Colors: 12)

If the name of the layer in the “Layer”-Dialogue should be printed in
bold, do

“Layer” → “Transparency” → “Add alphachannel”

Now go back to the “Layer”-Dialogue, duplicate the layer by right-clicking on the active layer and choosing “duplicate Layer”. Then hide the upper of the two layers by clicking on the “eye”-symbol on the left. Before proceeding, make sure the lower layer is active again!

Use the Blur-filter to make the colors merge at the edges.
“Filter” → “Blur” → “Gaussian Blur”:
Radius: 1x
Method: RLE

Next choose

“Filter” → “Artistic” → “Gimpressionist”
and use the following settings:

Presets
→ Feathers

Paper
→ Scale: 1x

Orientation
→ Directions: 6
→ Start Angle: 0
→ Angle Span: 120
→ Orientation: Adaptive

Size
→ Sizes: 4
→ Minimum Size: 3x
→ Maximum Size: 8x
→ Size: Adaptive

Placement
→ Placement: Randomly
→ Stroke Density: 36

The contours of the strokes are a bit hard, so reduce them by doing “Colors” → “Color to Transparency”: Color: #bababa

In the “Layer”-Dialogue, add a new layer and choose “Filling” → “White”, next move the newly created layer to the very bottom.

Now unhide the hidden layer in the “Layer”-Dialogue.

Now draw the outlines of the shape by doing
“Filter” → “Find edges” → “Neon”

Radius: 0.5x
Intensity: 0%

We don’t want any colored lines, so choose
“Colors” → “Desaturate”: Grauwert: Average
to remove the colors.

Next, we invert the colors in order to make the white lines become black “Colors” → “Invert”

We don’t want any gray tones, but black and white ones, so do “Colors” → “Threshold”: Move the handle about in the center of the color-bar or wherever you think the shape is clearly drawn by the lines or just leave the default
settings.

It should look like this now:

Next we are going to make the lines “pencil-like”.
“Filter” → “Artistic” → “Van Gogh (LIC)”
leave any settings at the default values

Remove the white background-color “Color” → “Color to transparency”: Color: #ffffff

Now use the rubber-tool to remove artefacts, just keep the “pretty” lines.

Finish the painting by choosing “Overlay” for the active layer in the “Layer”-Dialogue.