Math-as-Art

Arizona Desert

z = (x-y)/(sin(x)+1/cos(y))

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Reminds me of Sedona, and all the westerns filmed there.

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.

Bed o' Nails

z = sin(4y)+cos(4x)

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Looks like nails. Actually, this is the simple egg carton plot graphed at a different scale.

Big Ball of String

tan(rxcos(rysin(rx))) = xcos(y)

Beautiful symmetry.

Black and White Harlequin

sin(x+π/2) < cos(ry/10)

Nice!

Blue Signal

Density plot: z = sin(x)^2*cos(y)^2

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Simple expressions with interesting graphs are the best.

"Things should be as simple as possible, but no simpler."

Bluish Band-Aid on Black

Density plot: z = 2arcsin(cos(.5x^3))+xyarccos(x+y)^7

Black graph paper is at least beautiful, if not practical.

Bubbling Mesa

Graph and contour plot: z = xysin(x)sin(y)

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Dynamic, dream-like. Contour plot reveals multiple symmetries.

Carpet

rtan(sin(x)+cos(y))^2 < xlog(y)

Reminds me of a rug design, somehow.

Celery Row

z = sin(x)cos(y)/(x-y)

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Mathematical veggies.

Cells Under Magnification

Density plot: z = sin(ncos(x+y)/tan(xy))

Note the intricate complexity of material within cell walls (like real cells).

Chain-Link Fence

sin(1.5y) = cos(πsin(x))

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As kids, we would climb all over these.

Checkered Squeeze

1200sin(y)cos(x)/tan(x/y) < rcos(sin(x/y))

1200 was the most satisfying coefficient.

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/]

Corrugated V-Roof

z = abs(sin(2x)-y)

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Like the inexpensive, corrugated metal roofs covering many Balinese homes, including that of my in-laws.

Crazy Waves

Graph and contour plot: z = sin(ysin(x))/cos(cos(y))

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Interesting point symmetry. Nice contour plot.

Curtains

tan(x)cos(rysin(x)) < xcos(y)

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At the opera ...

Plush.

Dangling Green

Density plot: z = tan(x)sin(y)cos(xy)

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Houseplants?

Really like this one. Curious mid-century aesthetics. Reminds me of "cartoon art" of the 1960's.

Diffraction 1

cot(sin(xy)) < tan(cos(xy))

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Interesting diffraction effects caused by the limited resolution of the graphing tool.

Diffraction 2

cos(sin(xy)) < sin(cos(xy))

Cool diffraction patterns.

Diffraction 3

Density plot: z = 0.5sin(xyarctan((x/y)tan(x/y)))

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A complex expression. Zooming out creates a series of interesting diffraction patterns.

Dimpled Vase

z^2 = x^6-x^2+y^6+y^2

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I was utterly surprised by this plot. Reminds me of ceramic art.

Double-Back

r = t^2-t

𝜃 = tsin(t)

t = {0..40}

Intriguing variation on the spiral theme.

Dripping Paint

tan(.5ycos(x)) ≤ -cos(sin(y-2x))

I owned and operated a house painting business as a young man. Before sprayers, it was all rollers and brushes. Dried drips were a scourge.

Shaded areas of the plot above were too complex for Desmos to graph. Makes a nice effect.

Eccentric Symmetry

tan(sin(x^2)-2cos(x)-y^2) < 1

Curiously symmetrical.

Egg Carton

z = sin(x/2)+cos(y/2)

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Who doesn't like eggs?

Egg Carton Contours

Contour plot: z = tan(xy)sin(y)cos(x)

4-up collage of egg carton contour plots.

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.

Eye of Red

cos(ry^2+x^2) < 0

Had to use a close zoom, otherwise the shimmering effect was too annoying. As it is, it's just stimulating enough.

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).

Fancy Lapels

z = arcsec(sin(1/x)-cos(1/y))

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Sartorial aesthetics.

Fender Butterfly

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

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Redolent of butterflies and Fender guitars.

Gaping Maw

Graph and contour plot: z = (x^2+1.5y^2)e^(-x^2-y^2)

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An alien mouth? Cool contour plot.

Green Belt

Density plot: z = y(arcsin(cos(x^2)))+x(arccos(y^2))

Nice point symmetry.

Green Checkers

Density plot: z = tan(xy)sin(y)cos(x)

Anyone for checkers?

Green Longhorn

Density plot: z = arcsin(ncos(x)+y)/tan(7.1xy)

Exquisitely symmetrical.

Grey Vibrations

ycos(x) ≤ xcos(y)

I wish this thing would hold still ...

Hills and Valleys

Graph and contour plot: z = -xye^(-x^2-y^2)

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Pleasing balance.

Laser-Etched LP

Density plot: z = sin(x)^2-cos(y)^2

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Reminds me of the laser-etched version of the True Colours LP released by New Zealander pop group Split Enz in 1980.

An awesome record, both musically and physically. When light shined on the rotating lp, the reflected laser-etched designs would dance around the room.