Math-as-Art: Grapher

Showing posts with label Grapher. Show all posts

Bamboo Forest

Density plot: z = sin(2x)-cos(x/2)+tan(x)

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It took a long time to find just the right zoom on this one.

Notice the extreme scale. In the end, I went north of 10^120 before being satisfied that I'd found the best possible zoom.

Apparently, working with numbers 100 times larger than a trillion-trillion-google was a bit too much for the software. I broke Grapher in the process, and will have to reinstall it.

Worth it!

Basket Math

y = sin(13t)
x = cos(11t)
t = {0..2π}

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Hypnotic.

Controlled Chaos

x^3 = 1+7tan(xy^2)

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??

Convergence

y = kx/3
k = {1..18}

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Dirt-simple linear equations. Interesting effect.

[Idea borrowed from another math artist: https://samjshah.com/2013/01/08/families-of-curves/]

Double-Back

r = t^2-t

𝜃 = tsin(t)

t = {0..40}

Intriguing variation on the spiral theme.

Electric Rain 1

Density plot: z = sin(x)+cos(3x+y)

One problem with Grapher is that it's a bit unstable. Changing window dimensions will force a recalculation, and you end can end up with a completely different picture, unable to return to the original.

Such was the case with this relation, but I ended up with a couple of nice plots, anyway.

Electric Rain 2

Density plot: z = sin(x)+cos(3x+y)

A different zoom.

Falling Water

sin(y) = -1.5+e^-sin(kx)
k = {1..3}

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Reminds me (again) of mid-century design. Not chaotic (focus on one color at a time).

Fender Butterfly

r = sec(x)
y = tan(x)+cot(x)+k
k = {-5..5}

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Redolent of butterflies and Fender guitars.

Line Dancing

cos(x^2)+sin(xy)+tan(y^2) = 1

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Nice movement. Elusive symmetry.

Ripples

sin(xy) = cos(y)+sin(x)

Weird, wonderful asymmetry.

Slinky

x = sin(t^2)

y = cos(t)

t = {0..10}

Those of us "of a certain age" remember playing with thin, metal Slinky Toys as kids. A favorite trick was getting it to walk down stairs, unaided.

Invariably, they'd get tangled up and thrown out.

Sloppy Handwriting

xln(sin(y)) = ±ylog(cos(x))

You never know what a given graphing tool will throw at you!

The peculiar limitations of each tool are an integral part of the creative process. This plot looks markedly different in Pacific Tech Graphing Calculator, for instance (see Practicing X's).