I am so happy Vandorn Hinnant sent me an invitation to his current solo exhibition “The Hidden Mathematics: a surprising connection between Math and Art” at The New York Hall of Science. This was my first visit to the Hall of Science located in a stunning 1964 World’s Fair building in Corona Queens NY. I had wanted to see the museum’s permanent “Mathematica” display for a long time but it was an amazing discovery to find out about their art galleries. What a great place to see Math Art!
Hinnart’s artistic practice is a perfect example of the visualization of meta-mathematics. Interested in exploring mathematical geometric as complete systems, his drawings achieve detail and accuracy relying only on the construction rules of Euclidean geometry using a straight edge and a compass.
Inspiration for these drawings and paintings come from numerous mathematical sources including the Fibonacci numbers, the Golden Mean and fractals.
“Navigator’s Song” from 1995 features both horizontal and vertical lines of symmetry as well as isosceles triangle forms.
“Aromatic Vortex in Red & White” from 2012 depicts a rotating series of equilateral triangles to build a spiral, referencing the Padovan sequence.
Hinnant credits the work of numerous historical figures in the development of his decades long creative process including Pythagoras and Buckminster Fuller.
Kelsey Brookes current solo exhibition at the Jacob Lewis gallery is titled ” The Mathematics Underlying Art”. I was so happy to see that the Fibonacci Sequence is a major theme for these large scale paintings. Each square canvas is divided into thirteen (13 is a Fibonacci Number) wedges radiating from the center point. Then dots are made along each dividing line at intervals that correspond to the Fibonacci Sequence.
”1.618 ( Golden Ratio) Indigo”, 2017
An intricate concentric pattern is painted around each dot, filling the surface. The waves and undulations in this detailed work allude to the fact that Brookes is also microbiologist.
”1.618 ( Golden Ratio) Indigo”, 2017 (detail)
There are two sets of systems at work in this series. There is the overall predetermined structure, which features order 13 rotational symmetry and the uses the Fibonacci Sequence and the Golden Ratio to place each circle. Within this architecture,when you look more closely at the paintings you see the freer, expressive style . The mathematical structure creates a sense of order to contain the movement of the patterns.
“1.618 (Golden ratio) Red” 2017
The exhibit “Arte Povera” curated by Ingvild Goetz at the Hausser & Wirth Gallery
celebrates the 50th anniversary of the Italian artistic movement. Curator Germano Celant came up with the name “Arte Povera” which translates to “Poor Art”. Although the artists in the group had different practices, they were united in their rejection of the commercial leanings of Western art and chose to use everyday or “poor” materials in there work. Although a number of the artists made mathematically influenced work, Mario Merz offers the most direct connections. Merz created a large body of work over many years based on the Fibonacci Sequence.
This large wall installation from 1991 titled “Crocodilus Fibonacci” features the sequence’s digits in neon lights.
Here are some examples from a portfolio of lithographs based on the Fibonacci sequence and the growth patterns of plants “Da un erbario raccolto nel 1979 in Woga-Woga, Australia” (From an herbarium gathered in 1979 in Woga-Woga, Australia) .
All pictures courtesy of the gallery.
Once again there was a lot of interesting art on display at the Bridges Conference this year. Way to much to write about in my blog. To see more work the entire gallery is available on the Bridges website.
It is always difficult to pick a few pieces, but I will choose six over two blog posts.
Veronika Irvine’s sculpture “Delle Caustiche (Sagittarius Star Cloud)” incorporates the art of bobbin lace making into a 3-D surface. The hexagonal lace pattern has been altered to create a disc formation with larger hexagons at the outer edge of the curves. It required 3 rotations of this disc process. Copper wire has been used to give the lace structure. Irvine’s intricate band of lace graceful curves up and out of the plane.
Guy Petzall’s “Obloid Whorl” pop-up model is masterful created, using a single sheet of paper. Cutting and folding along a grid format, Petzall creates what he refers to as “a whorling meander motif”. The flat paper has been transformed into a rising spiral.
Lee Angold used water-soluble carbon to hand paint “Pinus nigra”. It is a an exploration of Fibonacci spirals found in cones of the Austrian pine, but with a twist. Cones with imperfect Phylotaxis are also included.
The Haber Space at Central Booking Gallery on the Lower East Side is currently presenting “Natura Mathematica”, curated by Maddy Rosenberg. This exhibition features the work of 24 artists and addresses the connection between the aesthetics of Mathematics and forms and patterns found in nature.
Erik Demiane & Martin Demaine, “Phylotaxis 959”, 2017
Picture courtesy of the gallery and the artists
Erik and Martin Demaine’s folded paper sculpture titled “Phylotakis 959” explores the Fibonacci double spirals found in sunflowers.
Amber Heaton, “Breakdown”, 2015
Picture courtesy of the gallery and the artist
Amber Heaton’s installation “Breakdown” also utilizes the Fibonacci Sequence. The number of strings in each vertical column increases from the outer edge on each on the perpendicular walls. Starting on each side with one thread, then one thread again, then 2, 3, 5, 8, 13, 21, 34, then 55 near the corner. This work offers the viewer a very direct visual representation of the beauty of this growth sequence that is found in many natural phenomena.
Eva Mantell, “Untitled”, 2016
Picture courtesy of the gallery and the artist
Eva Mantell “microcosm” series presents 3-D geometric line drawings using straws. This example features a series of acute triangles of various sizes radiating out from the center of the form.
“Natura Mathematica” displays a differs collection of work offering a broad exploration of the connections of Mathematical sequences series and formulae and the natural word.
It is the first week of March, time for galleries from all over the world to display art at one of the half dozen large fairs in New York City. Since a lot of my own work involves paper, it makes sense that my first stop this year was the Art on Paper Fair. Here is just a quick overview of some of the work I thought had interesting mathematical connections.
As you walk into the large venue, you are greeted by Tahiti Pehrson
‘s three monumental paper towers titled “The Fates” , presented by Art at Viacom
This closer look shows the intricate paper cuts. Pehrson has used the Fibonacci sequence – obviously a favorite of mine – to develop a pattern of concentric circles.
I found these two watercolor and pencil in the Cindy Lisica Gallery
booth. They are the work of Chun Hui Pak
. The top painting is titled “Iris Fold Watercolor 19”, the bottom painting is titled “Iris Fold Watercolor 13”. These works are 2-dimensional representations of a 3-dimensional origami sculptures. The square format is placed on a diagonal, emphasizing the order-4 rotational symmetry of the form. The geometry of origami folding is of great interest to mathematicians using shading techniques. Chun Hui Pak has given us a type of portrait of the paper folding.
has made a series of pen and ink drawings that incorporate grid structures. The Gibbons & Nicholas Art Gallery
has the drawing “Units 3” on display. The underlying squares of the grid anchor parallel sets of straight lines that create the illusion of volume in the rectangular cage, like a prism.
Although the focus of this fair is more specific to the materials used to make the art, there was a diverse selections of themes and forms represented. Art on Paper is open till Sunday March 5 2017.
Walking down Mulberry street I spotted this great sign in front of The Picture Room McNally Jackson Store.
The sign is the work of Benjamin Critton. It features a series of squares whose sides increase based on the Fibonacci Sequence. The first two squares are the same size. The third square has sides twice the side of the first. The fourth has sides three times as long as the first. This continues until the 7th square has sides 13 times longer than the first. They all are spiraled into a neat Fibonacci rectangle with sides in an 8:13 ratio.
Dikko Faust has been making prints using rectangular sections of grids and other geometric line patterns. By shifting the grids across the plane he has created a series of overlapping prints. Recently he has added a new twist to his process. Faust has invented a new printing tool that allows him to rotate the rectangle around a central axis point.
(A quick note about printers’ measurements: In the print studio distances are measured in picas and points. One inch is equivalent to 6 picas and 1 pica is equivalent to 12 points.)
To measure the rotation of the rectangle, Faust uses a straight edge to form a line from the bottom corner of the rectangle that is perpendicular to the horizontal bottom edge of his press, and then measures how far from the center point to the horizontal line. The initial measurement for a straight up and down rectangle would be 12 picas from the center (the rectangle is 4″x 6″ or 24 by 36 pica).
Faust has been experimenting with what happens to different patterns throughout the rotation process
To better explore the relationship between the grids,Faust has made series of two-color prints. He has selected only the prints that are the most visually interesting. Making consecutive prints with the number of ratio of pica differences to correlate with the Fibonacci Sequence is one technique.
The day I was in the studio, Dikko was working with a pattern he had created using airline (1/2 point) rules. He used parallel lines: there is 1 point of space between the first two lines, 2 points between the 2nd and 3rd line, then 3 points between the 3rd and 4th….. up to 6 points of space between the 6th and 7th line. Then the whole pattern repeats 12 times.
While I was at the printing studio Faust was making a single print with multiple rotational images. I took pictures throughout the process.
This is an early stage of the process: it has the original line print plus a 5 pt and 10 pt rotation clockwise and a 5pt and a 10pt rotation counter clockwise.
This is the finished print. There are 5pt, 10 pt, 15 pt, 20 pt, and 25 pt rotations in both the clockwise and counter clockwise directions. The process that Faust has developed to create these new prints is very algorithmic. It requires a commitment to experimentation trying different patterns and rotations. The outcomes are then judged on their aesthetic merit determining which prints are to be completed works of art.
The Cooper Hewitt, Smithsonian Design Museum in Manhattan was closed for renovation for three years before it reopened at the end of 2013. The current exhibition features an overview sample of their vast collection. I was very happy to discover that they have chosen to display quite a bit of work with direct Mathematical links. The debate over the critical delineations between Fine Art and Design is a hot button issue I am not going to address in this blog post. I have selected two pieces that have specific Mathematical themes.
“Prototype for an Environmental Screen, Fibonacci’s Mashrabiya”, 2009 is an architectural element designed by Neri Oxman at MIT Media Lab with Professor W. Craig Carter. It is was created using algorithms and digital processes but is based on traditional screens found in historic middle Eastern design.
The recursive Fibonacci Sequence was used to create the spiral pattern. Here is a detail of the center of the spiral.
Mathematician and artist Daina Taimina has been quite well known for her crocheted sculptures of Hyperbolic Geometry.
“Model of a Hyperbolic Space” 2011, is crocheted out of wool yarn. Working on these sculptures since 1997, Taimina has made major breakthrough on the modelling of figures in Hyperbolic space. Hyperbolic Geometry is a Non-Euclidean Geometry discovered by Janos Bolyai and Nicholay Lobatchevsky in the first half of the 19th century. In Hyperbolic Geometry each point has negative curvature and seems to curve away from itself.
At the Cooper Hewitt there were many more items that featured Mathematics as a design element. There was a very direct indication of the importance Mathematics plays in the field of both decorative and industrial design.
Summertime is a time to relax the rules. During most of the year my drawings require the use of grids and calculated templates. In the warmer months, when I am away from my studio, I continue to draw, but using a more organic approach. I have created two new types of small scale drawings based on the Fibonacci Sequence. These works are more about counted iterations then measuring. This allows the patterns to grow and develop more freely across the paper.
The first type of drawing I am calling Fibonacci Fruit. This type of drawing features pod-like forms with internal structures based on the consecutive terms of the Fibonacci Sequence. Here are two examples using the numbers 5 and 8.
In the first drawing there are 13 pods each divided into 8 segments and each segment contains 5 seeds.
The second drawing has 21 pods and again each pod has 8 segments with 5 seeds each.
Another type of new drawing I am calling Fibonacci Branches. In these drawings one branch divides into two new branches. Those branches each divide into three branches, then those branches each get five branches, then each of those gets eight branches until finally each of these branches gets thirteen new branches.1, 2, 3, 5, 8, 13. This creates a treelike arrangement.
In the next example, five sets of branches are scattered across the page. Each branch formation starts with one branch and grow in a similar fashion to the other drawing but in this case the final branch count is eight.
I am always interested in the negative space in my drawings. A good way to explore this is to make a white on black drawing.
There are still a multitude of possibilities for the continuation of these two drawing series. It will be exciting for me to see where the Fibonacci Sequence will take me next.