A Tip About a Mathematical Tit: 3D Graphs and Equations

If you want to draw a tit or a kind of “Dhul flan”, you can do it by typing this formula into Google (or copying and pasting it):

You can also test the original formulas directly in the interactive 3D viewer below.

The original 3D formulas

exp(-((x+60)^2+(y-4)^2)^2/999)+exp(-((x+4)^2+(y+4)^2)^2/999)+0.1*exp(-((x+4)^2+(y+4)^2)^2)+0.1*exp(-((x-4)^2+(y-4)^2)^2)

The image I obtained was something like this:

The original Google 3D graph of the first formula.

The image also contains a little green nipple adjacent to the tit, because this formula came from another that has two tits, and I left the nipple behind. The formula for two tits is:

exp(-((x-4)^2+(y-4)^2)^2/1000)+exp(-((x+4)^2+(y+4)^2)^2/1000)+0.1*exp(-((x+4)^2+(y+4)^2)^2)+0.1*exp(-((x-4)^2+(y-4)^2)^2)

Manipulating the formula

If you manipulate the formula, you can eliminate the nipple, as in the image below.

The graph after eliminating the separate nipple.

A mathematical basket and a meteorite

Feel free to manipulate the parameters of the formulas, and you will obtain different amusing images. For example, I managed to draw a kind of basket, and then I also drew a ball like a meteorite that is going towards the basket.

A ball like a meteorite. Visit the original ♥ChachoBiriukov site.

Try the equations in 3D

Choose an original formula, manipulate its parameters, then select Plot equation. Drag horizontally to rotate the graph; on a phone, vertical movements still scroll the article.

Equation: z =

Use x, y, exp, sin, cos, tan, sqrt, abs, log, ln, pi, e and + − * / ^. The ^ symbol means a power; exp(t) means e raised to t. The two presets preserve the original numbers, including x+60 in formula 1.

The original static graphs and formulas are available above.

Keyboard: focus the graph and use the arrow keys to rotate or tilt it. Home resets the view.

01

Preparing the graph…

View and plotting interval

Rotation Elevation Visual height

x minimum x maximum y minimum y maximum

Select Plot equation after changing the interval. To include the distant peak of formula 1, try x from −70 to 10. Visual height changes the presentation, not the equation.

More visual experiments

For another experiment in representing mathematics visually, see To mathematicians: Why does a 9 appear between prime numbers?, where I represent prime and non-prime numbers with coloured circles.

To compare this mathematical basket with a decorated household object and a digitally added basketball, see How to draw a vase with snakes and circles + basket ball.