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#AbstractArt

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"Study for Improvisation 3," Wassily Kandinsky, 1909.

Here's our old pal Kandinsky, in his early Abstract period. Here he was focused more on visually capturing what he termed "the noise of emotion" and while technically abstract you can make out a horse and some human figures.

Experts claim that this is the Fourth Horseman of the Apocalypse, referred to in the Bible. This was the horseman Death, although he hardly looks funereal with all this color. But the horse is rearing rather than proceeding across what appears to be a white bridge; is the yellow fortress holding it at bay? Is that a blue figure seated to the right? What is its meaning?

Kandinsky had quite a few spiritual ideas but they're hard to fathom in his work. But it's an arresting image, nonetheless. It sold at Christie's for over $16 million in 2008.

From a private collection.

These artworks are based on a generalization of Lucas sequences for complex numbers, defined as:
Z(0) = 1
Z(1) = 1 or i
Z(n) = shrink( e^(iθ)·Z(n-1) + Z(n-2) )

Where shrink() is a function which decreases a complex number into the two-unit square or the unit circle centered at the origin. In these works I use three different versions, based on taking out the integer part of the real and imaginary parts (or the integer part minus 1), or of the modulus of the number in polar form.

Figure 1 depicts the 128 values walk using θ = π/5 and Z(1) = i, and the shrinking function which takes out the integer part of the real and imaginary parts.

In the three artworks that follow, the lines connecting successive values toggle between being drawn or not. See the alt text for more information related to the artworks.
#mathart #math #algorithmicArt #AbstractArt

Continued thread

The title refers to a phenomenon in neural networks where the training process for new tasks interferes with the model’s understanding of old tasks. Our insatiable desire for new technologies like AI accelerate climate change, leading to the destruction of our communities and loss of memory.