Diffusion drawing

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In London, there is a sculpture called Quantum Cloud, where the silhouette of a person emerges out of steel bars, arranged to mimic a random walk (see Fig. 1). This made me curious about how one might replicate this effect: using random walks to paint an image.

Quantum Cloud sculpture
Fig. 1. Quantum Cloud. Source: Wikipedia.

One possibility is to make the random walker spend more time in dark areas and less time in light areas. The trajectory of a two-dimensional random walker is described by the Langevin equation

\[ d\mathbf{r} = \mathbf{A}(\mathbf{r}, t)\,dt + \mathbf{B}(\mathbf{r}, t)\,d\mathbf{W}(t). \tag{1} \]

This corresponds to the Fokker-Planck equation

\[ \frac{\partial p}{\partial t} = -\nabla \cdot \left(\mathbf{A}(\mathbf{r}, t)p\right) + \nabla^2 \left(D(\mathbf{r}, t)p\right). \tag{2} \]
Showcase diffusion drawing
Fig. 2. Showcase diffusion drawing.
First failed diffusion drawing attempt
Fig. 3. First failed diffusion drawing attempt.
Second failed diffusion drawing attempt
Fig. 4. Second failed diffusion drawing attempt.
Full diffusion drawing result
Fig. 5. Full diffusion drawing result.
Pixelated image used for the diffusion drawing
Fig. 6. Pixelated image used for the diffusion drawing.
First refined diffusion drawing
Fig. 7. First refined diffusion drawing.
Second refined diffusion drawing
Fig. 8. Second refined diffusion drawing.
Animated diffusion drawing
Fig. 9. Animated diffusion drawing.