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I've recently been playing around with creating interesting art from mathematical functions using Rhino (3D Design) and Grasshopper (a "Parametric" programming language that works in conjunction with Rhino).  Some images are rendered in Keyshot8.

The Fractal images are programmed in Ultra Fractal.

## Mathematical Art

A vase designed with a beautiful repeating pattern.

"Icosahedron with Sierpinski Triangles" - Beautiful patterns on each of these 20 faces of the Icosahedron.

"Icosahedron with string pattern" - Beautiful interwoven patterns.

"Strung" - just an interesting shape made with straight lines.

"Swirl" - just a beautiful mathematical curve.

"Maelstrom" - just some cool shapes and patterns with neat coloring and texturing.

''Glass Coffee Table'.  A repeated, enlarged and rotated rectangular shape makes a nice coffee table.

''Sierpinsky Nested Triangles'.  Based on a fractal with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.

''Woven Pot'.  Just playing with woven patterns on a surface.

''Patterns'.  Just playing with a repeating pattern of a 4 star element.

''Topography'.  Just playing with repeating patterns, textures and my 3D modeling skills.

''Woven Spiral Artwork'.  Spinning a closed loop curve around a moving center point creates beautiful patterns.

''Pierced Cube'.  Just playing around with making a cube whose perforations are in inverse proportion to the distance from the top center corner.

''Julia Spiral'.  This image is a representation of a mathematical fractal pattern of the Julia set.

''Lambra Mandelbrot'.  This image is a representation of a mathematical fractal pattern of the Mandelbrot set.

''Fractal Reflection'.  Another Mandelbrot fractal pattern reflecting in water.

''Modern Sculpture'.  Just a fun sculpture and rendering project .

'Olympic Logo'.  Getting ready for the 2020 Olympics. For fun - just designed this logo.

'Interlocking Mobius'.  Another one of those cool math shapes - one infinitely long side and one infinitely long edge.

'Pantheon Dome'.  I recreated the Pantheon dome in Rome on my computer.  It was built almost 2,000 years ago and is still to this day the largest un-reinforced concrete dome in the history of architecture.

And, using the similar detail of the Pantheon - I created another cool surface shape.

'Woven patterns on surfaces'.

An example of how one can change the surface and texture of an object in software.

'The Queen's Chandelier'.  Just a fun geometric shape - that looked like the worlds most expensive chandelier when I finished.

'The Alexa II".  If Amazon wanted to upgrade their look to the Alexa Echo Dot - this might be it.

Fully programmed in Grasshopper & Rhino - Rendered in Keyshot8.

'Cubic Circulating Pump'.  Not really - just practicing my computer animation techniques.  Programmed in Grasshopper and Rhino.

'The Queen's Jewel Box'.  It you have a nice 12 carat diamond - this would be the perfect box to display it in.

'Sphere of Gears'.  This spherical surface has 92 gears.  60 brass (16 teeth), 12 Copper (20 teeth) and 20 Steel (24 teeth).  Perfectly arranged such that rotating any one gear rotates ALL the other gears on the sphere at the same time.  Inspired by the work of my talented friend Paul Nylander.

And the animated version of this Sphere of Gears.  Rendered in Rhino - Compiled in Premier.

Click on the image below to see the 13 second animation of this thing.

'Wave of Hexagons'.

Just a cool geometric pattern.

A 4-sided mobius curve with pattern.

An Enneper curve.

A 3D designed bracelet for my wife.

The rare "gold banded Ethiopian Nautilus" shell.

In fact - its so rare - only one exists - discovered in June of 2018 in my computer.

Designed in Grasshopper

A woven pattern of interlocking shapes creates a beautiful surface pattern.

"Star of David".  The 6 elements of the shape on the inside swirls around underneath and comes up to form a Star of David.

"String over Onyx ball"

"Cube of Cubes"

"The Orb"

"Neon Light through Field of Pyramids"

"Voronoi surface on Torus"

"Cubic repetition"  (Two variations)

"Dodecahedron with Crazy Spirals

"Mathematical Shell"

"Torus Knot".  Programmed in Wings 3D

"Loop-d-loop".  A Trefoil knot shape made of a grid structure with red ball which rolls around inside.

"Twisted Surface".  When you bevel, carve-out and twist edges, faces and the elements of a cube enough times, and then smooth it all out, you can get some interesting shapes.  Programmed in Wings 3D

Twisted Pyramid.  The Outside becomes the inside becomes the outside.

A Wind Chime.

This is just a made up image.  I wanted to  play with color and lighting in a water environment.

"Floating Treasure".

This was just for fun - I call it the 'Evening out on the town'.

A little bit of artistic work on a mountain range of mathematical functions.

This is a Dodecahedron (12 sided polygon) with spirals on it.  Each spiral arm connects to another spiral arm on adjacent or opposite faces - yet never touches any other one along the way.  (That was the hard part).

Imagine setting out from the equator heading 30' North.  If you keep heading at 30' (or any other constant angle), you will get very close to the north pole - without ever getting there. That is called a Loxodrome path.  Here are 4 Loxodrome paths on this globe, with a light next to one of them showing the cool shadow patterns you get on a surface from that light.  Inspired by my friend Paul Nylander.

I actually 3D printed this and have it with a real light shining on my wall in my workshop.  Cool.

I set out to print the Hebrew, Greek and Aramaic names of God from the Bible on the inside of a spiral that wraps around creating a sphere.  The 'Hidden Names of God'.  Just sent the file to the 3D printer to be printed.

See the Projects tab for the final 3D printed image.

Imagine a spherical shape with distorted cut-outs, that when a light is put inside - the projections on the table surface make a perfect set of squares.  This is such a shape.  Just sent it off to be 3D printed.

Inspired by Henry Segerman.

Here is a series I call my 'Floating Orb' series

Using Grasshopper, I programmed a glass sprial to wrap around a marble torus.

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