Similar to the difficulty of formally proving the hash visualization properties, proving that all the images generated by Random Artare regular, is hard. However, in practice we can limit the depth of the expression tree, which also limits the complexity of the image. Another factor limiting high complexity is that every function has the same domain and range, which is the interval . Hence, there are no problems with functions approaching infinity, with a subsequent sin function, resulting in a very high frequency signal. In practice, we use 12 for the depth of the expression tree, which has so far resulted in regular images.
As we have shown earlier, we can use the Fourier spectrum to detect irregular (or noisy) images. In figure 5 we show two Random Artimages with their corresponding Fourier spectrum. Our first observation is that the resulting Fourier spectra are favorable. They resemble the spectrum of a real image (as shown in figure 1(d)), as the energy is concentrated in the low-frequency components. However, image 5(a) is much noisier than image 5(c), as the energy spectrum has more energy in the high frequency components, which can be observed from the corresponding Fourier transforms.
Figure 5: Random Artimages with frequency spectrum
Another issue is to ensure that the resulting images are not too simplistic. We have discussed two ways how to detect simplistic images. One method is compression, where we reject images which compress too well, and the other method is again the Fourier transform, where we can infer simplistic images if all the energy is in the lowest frequency components only.
To get an estimate of how many images in practice are regular or simplistic, we generated 100 images and inspected them manually. It turned out that all images were regular and only 2 were simplistic. This shows that we can generate regular and minimally complex images by detecting and rejecting infrequent outliers.