Random Spheres

Requires a Wolfram Notebook System

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Edit on desktop, mobile and cloud with any Wolfram Language product.

Create artistic three-dimensional configurations with up to 800 colored spheres.

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Random and nonrandom tools are provided.

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Contributed by: Karl Scherer (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

"Amount" setter bar

Select the total number of spheres.

"Randomize" option

Clicking these buttons randomizes the positions, radii, and color of the spheres.

The positions of the spheres are controlled with the "configuration" options.

"Configuration" options

"Box" is the default. During randomization the centers of the spheres are randomly positioned inside a box of size 10×10×depth.

"Ellipsoid" randomly places the centers of the spheres on an ellipsoid inscribed in a 5×5×depth/2 box. Depth 0 gives a disc and depth 10 gives a ball.

"Tube" randomly places the centers of the spheres on a cylinder with radius 5 and a height of "depth". Choosing a tube with depth 0 shows a torus shape.

"Cone" randomly places the centers of the spheres on a cone of radius 5 and a height of "depth".

"Spiral" randomly places the centers of the spheres on a cylindrical spiral with radius 5 and a height of "depth".

"Double helix" will randomly place the centers of the spheres on a double helix with radius 5 and a height of "depth".

The more spheres you use, the more these configurations take shape. Explore!

"Depth" slider

This option is the height control of the selected configuration. This "depth" option only applies to the randomized positioning of all spheres. It does not restrict the setting of the coordinate of a single sphere; see below.

"Radii" options

Option "+" will multiply each sphere radius by 6/5. If the result is greater than 10, the radius will be set to 10.

Option "-" will multiply each sphere radius by 4/5.

Option "=" will give each sphere the radius of sphere number 1.

"Specularity" slider

Controls the specularity (shine) of the spheres.

"Lighting" options

You can choose between "automatic" and "neutral".

"Background"

Sets the background color.

"Axes" option

Displays the , , and axis.

"Plot range" options

"All" always displays all spheres in their entirety. This might cause the view to change when you enlarge a sphere, etc.

"Fixed" always shows the same view of all data displayed in a 14×14×14 box (containing the 10×10×10 plot range). Very large spheres might be partially cut off.

The following options control single spheres:

"Sphere"

Here you choose which sphere you want to edit.

"Color"

Here you can choose a new color for a sphere. The new color will only be visible once you have moved the sphere.

"r", "x", "y", "z"

Here you can edit the radius and , , position of the selected sphere (all values are between 0 and 10).

Hints

To zoom in and out, hold the Ctrl key with the mouse button pressed while you move the mouse up and down.

To pan, hold the Shift key with the mouse button pressed while you move the mouse.

Remember that no sphere can be placed outside the box 10×10×10.



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