Arizona Desert

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


A favorite.

Bamboo Forest

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


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

Notice the extreme scale. In the end, I took north of 10^125 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 actually broke Grapher in the process, and now will have to reinstall it.

Worth it!

Blue Signal

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


Simple expressions with interesting graphs are the best.

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

Bubbling Mesa

z = xysin(x)sin(y)


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


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


Reminds me of a rug design, somehow.

Celery Row

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


Oprah loves bread (duh). I love veggies.

Cells Under Magnification

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


Intricately complex inside the cell walls. Seemingly random, yet strangely ordered, as with the innards of real cells.


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


Dirt-simple linear equations. Interesting effect.

{Note: This is original work, but I stole the idea from another math artist. Forgot who.]

Corrugated V-Roof

z = abs(sin(2x)-y) 


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

Crazy Waves

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


Interesting point symmetry. Nice contour plot.


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


At the opera ...


Dangling Green

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

Curious mid-century aesthetics. Reminds me of cartoon art of the 1960's.


Diffraction 1

cot(sin(xy)) < atan(cos(xy))


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)))


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

Dimpled Vase

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


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


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))


Owned a house painting business as a very 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)


Who doesn't like eggs?

Electric Rain 1

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


One problem with Grapher is that it's unstable. Changing the 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 just too annoying. As it is, it's just stimulating enough.

Falling Water

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


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

Fancy Lapels

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


Sartorial aesthetics.

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)


This one's a shout-out to an old music buddy, Nicolas Del Drago.

Grey Vibrations

ycos(x) ≤ xcos(y)


Be still!

Hand-Drawn Hilbert


You can draw fractals by hand, if you have the patience. The Hilbert Curve above is one continuous line. (Can you find its endpoints?)

Lots of us doodle using fractal designs, for instance. (Do you?)

Hills and Valleys

z = -xye^(-x^2-y^2)


Pleasing balance.

Lawn Chair

z = x^2-y^5+cos(arcsin(cos(y)+sin(x)))


Add a simple frame, and this would make a fine garden chair, with holes to enhance air circulation.