It took me 30 years to find a way to generate the greater reality of one-sidedness beyond the Mobius strip - the Metamobius algorithm. The Tc S3 m2 is the first surface I generated with it (2010). When I saw it materialize I was beside myself with delight and awe. The constraint of one-sided surfaces having to be a strip had finally been broken. It was one of the happiest moments of my life. After staring at its beauty for the longest time I got up from my chair and danced around the room - a dance I am forever grateful no one witnessed.  

The Metamobius algorithm also generates fundamental two-sided surfaces. The T5 m2 = O b6 is a beautiful example of one of these. The algorithm has many variables that can be adjusted to produce an endless variety of one-sided and two-sided surfaces. One option is to produce either a symmetrical or asymmetrical surface. After creating the Metamobius algorithm I spent the first while mainly applying it to symmetrical surfaces. Later I began generating asymmetrical one-sidedness, and I was immediately fascinated with the beauty of broken symmetry within this kind of geometry.  

The Sc T2 S2 m2  is an example of a Metamobius surface that is diagonally symmetrical. It is also an example of how all of these beautiful surfaces have taken on a life of their own as an art form. 

Adding two colours to a one-sided surface was a bit of humour. It forces the eye to see two sides, although when you look closely, somewhere the two colours have to meet.

The Pc S5 m2 is a remarkable one-sided surface that is delightfully symmetrical. The underlying concept with the Metamobius algorithm is the use of space as a substructure upon which to build the actual surface. In this case the space substructure was my first attempt at a more complex form of space and has since led to many wonderful insights about the nature of both symmetrical and asymmetrical one-sided surfaces. 

The T1 lv3 m2 (Charlotte) is a wonderful example of containing the entire one-sided surface within a circular or spherical boundary. Using the Metamobius algorithm, any surface can be converted likewise. This is a fascinating aspect of this method. Take a look at any of the surfaces here on the site and imagine them being transformed into an entirely enclosed spherical surface. 

Asymmetrical Metamobius surfaces are generated from asymmetrical space substructures. The Pc T3+S2(alt) m2 is a beautiful example of this kind of one-sided surface.

A beautiful example of one-sided symmetry.

I added colour to the Tc T1+S2 to emphasize its heart shape - nice for Valentine’s Day.

The Metamobius algorithm can connect individual one-sided surfaces (metamobs) to form beautiful landscapes of one-sidedness. Here is a simple one connecting two Tc m2’s at each end with a Tc S3 m2 in the middle.

The algorithm is powerful - it generates and topologically categorizes the entire greater reality of one-sidedness.

A reconnaissance satellite captured this image of a Metamob from the planet Metamobia orbiting Earth. It came in peace, delivering a message to humankind: "We are all on the same side".

No matter how you distort a Metamobius surface (a metamob), it maintains its original topological classification (the right side of the equal sign in its name). See the original Pc T3+S2(alt) m2 = n b2 x-5 n5 t24 here in the Gallery. See also the Metamob from Metamobia :-)

Metamobius surfaces can be connected in various ways to form more complex landscapes of one-sidedness. Here three fundamental surfaces called Tc m7’s are connected to create a whole new, beautifully flowing one-sided surface.

The beauty of one-sided symmetry…