Blue Moon shows how one, two, three and four
circles can be drawn so that they do not intersect one another (they could be
nested, one inside the other). The sequence generated by non-intersecting
circles is 1, 2, 4, 9, 20,48,… etc.

Blue Moon shows the 16 possible arrangements
with 1, 2, 3, and 4 circles.

Moon Gazing 5

30" x 24" Charcoal and acrylic on canvas, 2018

Moon Gazing 5 shows the 20 arrangements of 5 circles so that no two circles intersect though
they can be nested one inside the other.

Arrangement

54"x28", Acrylic on canvas, 2016

This is an arrangement of the terms 0 to 74 of the sequence A238191 which is the sequence of the digital roots of the partitions of numbers. In this arrangement, I have started from the top right corner and gone in one direction until I have come to the edge of the canvas evenly when I have changed direction.

Arrangement 2

(Dawn to Dusk)

24"x 22", Acrylic on canvas, 2017

Concatenated Square Numbers

30" x 18", Acrylic on Canvas, 2011

I was fiddling with some numbers one afternoon and started with a string of square numbers 1,4,9,16,25,36,49,….pulling and pushing them around to see how they behaved. I decided to concatenate them 1,14,149,14916,1491625,149162536,….These quickly became too big for me to handle so I then cut them down to size by taking their digital roots 1,5,5,3,1,1,5,6,6,7,2,2,9,7,7,2,3,3,4,8,8,6,4,4,8,9,9... and realised that they form a beautiful repeating sequence. This work is inspired by the 27 terms which form the repeating sequence. There is light at the end of the tunnel.

24 Sums of Fibonacci

26" x 18", Acrylic on canvas, 2010

The digital roots of the Fibonacci Sequence repeats after every 24 terms and the repeating sequence is 1,1,2,3,5,8,4,3,7,1,8,9,8,8,7,6,4,1,5,6,2,8,1,9.

The 9 Digital Roots of Triangle Numbers

24" x 26", Acrylic on canvas, 2011

The Triangle Numbers 1,3,6,10,15,21,28.... have digital roots which are always 1,3,6 or 9. In fact, they form a repeating sequence of the following: 1,3,6,1,6,3,1,9,9...

Meditations on Symmetry

36" x 30", Acrylic on canvas, 2012

The Triangle Numbers 1,3,6,10,15,21,28....are an increasing sequence. Concatenated triangle numbers are 1,13,136,13610,1361015, 136101521,....another increasing sequence. The digital roots of the concatenated triangle numbers generate the repeating sequence 1,4,1,2,8,2,3,3,3,4,7,4,5,2,5,6,6,6,7,1,7,8,5,8,9,9,9,... This work is a meditation on that repeating sequence.

Pentagonal Numbers

20" x 18", Acrylic on canvas, 2011

Hexagonal Numbers

24" x 26", Acrylic on canvas, 2011

Heptagonal Numbers

34" x 24", Acrylic on canvas, 2011

Octagonal Numbers

20" x 18", Acrylic on canvas, 2011

The Octagonal numbers are 1,8,21,40,65,96,133,176,225,280,341,408,481,560,645,736,833,936,1045,1160,...

When the digital roots are taken, they form a repeating sequence1,8,3,4,2,6,7,5,9,...