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#mathart

30 posts26 participants1 post today
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Microfractal

Decagon (fractal version)

\(z_{n+1}=fold(z_n)^2+c\)

where fold is a generalized absolute value function. A complex number has two components: a real and an imaginary part.
If we take the absolute value of one of these parts, we can interpret this as a fold in the complex plane. For example, |re(z)| causes a fold of the complex plane around the imaginary axis, which means that the left half ends up on the right half. If we do this for the imaginary component |im(z)|, we fold the complex plane around the real axis which means that the bottom half ends up on the top half.
These two operations are quite similar, because the imaginary fold is just like the real fold of the plane, except that it was previously rotated 90 degrees (z * i). But what if we rotate the plane by an arbitrary number of degrees?
An arbitrary rotation of the complex plane can be expressed as rot(z, radians) = z * (cos(radians) + sin(radians) * i), where radians encodes the rotation.

The image here is produced, by rotating the plane exactly five times, and folding the imaginary part each time.

I found this algorithm in the Fractal Formus under the name “Correction for the Infinite Burning Ship Fractal Algorithm”.
It can be seen as a generalization of the burning ship obtained by folding the complex plane twice with a rotation of 90 degrees, i.e. folding both the real and the imaginary part.

Black fractal structures on a mostly green background, rendered using distance estimation.
#fractalfriday#fractal#burningship
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Joy of Randomness (Rachel)

I've been pen plotting a lot of postcards this year. I love it because 4"x6" is small enough that the post cards are quick to make. This allow for really quick iteration of ideas and exploration.

While one postcard is being drawn by the plotter, I am often exploring a variant and come up with what I want to see next. My poor plotter has gotten very little rest.

The speed and size also makes it lower stakes and encourages me to be bold and "mess up". As much as mistakes are possible in art.

The code for these postcards was written in a mix of python using @abey79's Vsketch library and javascript using the new p5.js pen plotter svg library by @golan. So much gratitude to all the work on both of those.

a 11x9 grid 4"x6" post cards on a wooden floor with colorful art in several styles. Some are variants of perlin noise flow fields, some are are overlapping circles, some are squares in a grid.
a 3x3 grid of 4"x6" pen plotted post cards. Each post card has drawings of squares. Some are in a grid with no overlap. Some are in a grid with overlap. And some are in what looks like a pile all on tope of each other. Several use a blue purple color scheme.
A 2x2 grid of 4"x6" pen plotted post cards. All drawn the same blue, green purple fine tip pens. Top left is a field (magnetic not grass) with several spots of varying sizes of concentric circles and rounded lines between them. Top right is flow field with densely drawn lines making a wavy pattern. Bottom left is a flow field with looser whipy waves. Bottom right is a flow field with densely drawn lines making a wavy pattern with a few whirlpool spirals towards the bottom left.
a 3x1 grid fo 4"x6" post cards. Each of most of the post cards is filled with curved lines. Top: pinkish red lines coming in to at various angles to form a few very tight spirals. The centers of the tight spirals is a small irregular darker red spot. Middle: Green lines with about 10 spots the lines avoid and go around like water would be diverted by rocks. Bottom: pinkish purple. Similar pattern to the middle one but in purple instead of green and spots in different places in the image.
#penplotter#mathart
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