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#mathart

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Dani Laura (they/she/he)

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

A chaotic zigzag line, starting at z=i (top middle), initial colour is red and then follows the hue circle.
"Dreadful Subconscious". Here θ = 1 radian, Z(1) = i, and the shrinking function makes the two-unit square similar to the surface of a torus. Chaotic straight lines drawn on top of each other of successive colours black, purple, and orange over white background.
"Not your gender". Here θ = π/17, Z(1) = 1. Chaotic straight lines of many colours drawn on top of each other, usually they do not change quadrants, so four distinct colourful "squares" can be seen.
"You have been warned". Here θ = π/5, Z(1) = 1. Similar pattern of previous artwork, but here each quadrant has roughly the same proportion of colours. Lines are in colours cream, black and reddish over white background.
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foldworks

@ark_brut A bit beyond my current skills, so I looked for something much simpler: youtube.com/shorts/g0-eD9c5uog. I used four lolly sticks and two rubber bands lying around the kitchen.

The only tricky part was cutting the notches with a craft knife and a self-healing mat.

I might try other tensegrity structures, but some need holes like the bed slat structure which is a step up in terms of equipment and skills.

A tensegrity structure on a red background. It is made from four lolly sticks and two blue rubber bands. Three sticks form an equilateral triangle; the fourth stick is held by the rubber bands through the centre of, and perpendicular to, the triangle.
#tensegrity#geometry#MathArt
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