Virtual Gallery

Fun with Fractals and Other Mathematical Quilts

Partial sponsorship provided by

Reynolds and Associates PLLC

Exhibit curated exclusively for the Texas Quilt Museum

Elaine Krajenke Ellison of Sarasota, Florida, a retired mathematics teacher, is an author and lecturer who creates unique quilts inspired by a variety of mathematical topics. Beginning in childhood, her artwork has included sculpture, drawing, painting, and stained glass. Around 1980, Ellison began to concentrate on cloth as her preferred medium. She has created nearly 70 quilts spanning 4,000 years of mathematics, and she co-authored Mathematical Quilts and More Mathematical Quilts, geared toward K-12 students. Currently, she is working on a quilt based inspired by the mathematician Baudhayana, who lived in India during the 8th century B.C.E.

During his illustrious career as a physics teacher at West Texas A&M University,

Dr. Vaughn Nelson of Round Rock, Texas, now an Emeritus Professor, published several books on alternative energy sources, especially wind power. His latest book, published this year, is Innovative Wind Turbines: An Illustrated Guidebook. He received three awards from the American Wind Energy Association, one of which was the Lifetime Achievement Award in 2003, and was named a Texas Wind Legend by the Texas Renewable Industries Association in 2010. Dr. Nelson created his first quilt in 2006, using a design he created with Penrose Tiles pieced by his wife Beth and longarm quilted by his daughter, Alisha. Then, he caught the “quilting bug” in earnest, making more than 150 quilts that he has designed, pieced, and quilted. Dr. Nelson’s intriguing quilts in this exhibition intertwine science and art with colorfully dramatic effects.

GREEK CROSS TO

SQUARE DISSECTION

53” x 53”

Year Completed: 2013

Made by: Elaine Krajenke Ellison

The Bridges Conference in 2008 met in Leeuwarden, Netherlands. A paper presented at the conference titled “Making Patterns on the Surfaces of Swing-Hinged Dissections” by Reza Sarhangi caught my eye. In the paper, Sarhangi mentioned a powerful technique for dissections, which originated in the book Dissections, Plane and Fancy by Greg Frederickson.

The technique is to superimpose two tessellations in a way that the common pattern of repetition is preserved. A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes called tiles. The tiles fit together so there are no overlaps and no gaps. The common shape in the entire quilt is a flag-shaped tile of six sides. The shape in my quilt is common to both the Greek Cross and the Square Cross. The idea of using two overlapping tessellating grids intrigued me, and the significant use of red was a challenge!

TILED TORUS WITH

CHANGING TILES

44” x 44”

Year Completed: 2009

Made by: Elaine Krajenke Ellison

Tiled Torus was inspired by the work of John Sharp, UK; Craig S. Kaplan, Canada; M. C. Escher, Netherlands; Douglas Hofstadter, Indiana; and William Huff, New York. Each of these individuals were interested in how tiles change as they move across the plane. More formally, the name parquet deformation applies to the tiles that change and continue to change as they tell their story. The idea for creating a quilt where the shape of the polygon tiles change was a fascinating one.

I was inspired by papers I saw presented at Bridges in Leeuwarden in 2008 and Banff in 2009. In playing with a design, I decided to color tiles that are the same with the same color. The colors gave a glowing, wavy effect to the overall look of the quilt. As the design was being drawn, I began to think that the opposite edges of the quilt could be mathematically "glued" to each other. I was correct! A donut-shaped object appeared. A torus is a three-dimensional shape made by revolving a small circle along a line subtracted from a bigger circle. A donut-shaped object results. This quilt is an example of a three-dimensional shape that is cut and laid flat.

SCHOOL OF FISH

60” x 54”

Year Completed: 2010

Made by: Elaine Krajenke Ellison

I have always found morphing designs very interesting. Attending a number of Bridges conferences (an annual event concerning connections between art and mathematics) left me wanting to design some morphs to be quilted.

School of Fish is a good example of a morph. To morph an object, one changes smoothly from one image to another by small gradual steps. This small change in each object can be done using computer animation techniques. In my design, these small changes were done in drawings by hand.

BUCKEYBALLS AND BUBBLES

30.5” x 50.5”

Year Completed: 2008

Made by: Elaine Krajenke Ellison

A revolution in chemistry began with the work of Richard Smalley and Bob Curl, professors at Rice University, and Sir Harry Kroto of the University of Sussex. Their work began in 1984, and in 1996 their discovery lead to a Nobel Prize.

In 1985, Smalley's team announced the discovery of a new pure form of carbon. For centuries, research showed that carbon came in just two basic structures: hard sparkling diamonds (carbon atoms are arranged in little pyramids); and dull, soft, slippery graphite (sheets of carbon-atom hexagons). This new pure form of carbon has the official name of buckminsterfullerene because it is shaped like the geodesic dome invented by Buckminster Fuller. Informally, scientists call the carbon molecule “buckeyball” or “C-60”.

To the mathematician, the buckeyball is wonderfully symmetrical, with 12 pentagons and 20 hexagons. The symmetry gives the buckeyball properties that are now used as: in chemical sponges, in drug design, chemical probes in a scanning-force microscope, in miniature circuits, lubricants, catalysts, superconductors, batteries, molecular sieves, and possible improved resolution in photocopiers. In the United States, Xerox owns the patents for using C-60.

FROZEN FRACTALS ALL AROUND

47” x 47”

Year Completed: 2015

Made by: Elaine Krajenke Ellison

A fractal is the result of a process that begins with a geometric figure (in this case an equilateral triangle), along with a transformation that is applied repeatedly to the figure. Fractals have fine structure, self-similarity, a size depending on the scale at which they are measured, simple recursive construction, and an organic appearance.

The movie Frozen inspired me to create this quilt. The colors in the movie were clear, crisp, and pure. For some time I wanted to generate a quilt using the grid of M. C. Escher's Print Gallery from 1956. Escher had created various perspectives along with interesting mathematics. I decided to place the Koch Snowflake in each corner of the grid. The Koch Snowflake was named after the Swedish mathematician Helge von Koch (1870-1924).

LIGHT ZERO

49” x 51”

Year Completed: 2006

Designed by: Vaughn Nelson

Pieced by: Beth Nelson

Quilted by: Alisha Nelson Miller, Kennewick, WA

This quilt is an example of Penrose Tiles which is fivefold non-periodic symmetry, that can cover the plane with two shapes. Piecing of the Penrose tiles was difficult because of their numerous Y-seams. Tiles were quilted in the ditch, and the border quilting resembles a jumble of photons. I made templates of the two shapes and then started with the fivefold star in the center. AccuCut now has custom dies available for these two shapes. Sir Roger Penrose (b. 1931) is a mathematical physicist who investigated non-periodic tiling in the 1970s.

BRILLOUIN BLUE

61” x 61”

Year Completed: 2009

Made by: Vaughn Nelson

Quilted by: Alisha Nelson Miller, Kennewick, WA

Brillouin zones consist of reciprocal lattice shapes, a patchwork of points and lines in momentum space representing Bragg diffraction planes in a crystal. These planes bisect a reciprocal lattice vector, at right angles.

This quilt provides a geometric description of the allowed states that electrons or phonons (vibrational energy) can occupy. Each fabric represents one zone; zones get smaller farther from the center. Each zone meets at a corner or an edge. Brillouin Blue has 8-inch blocks. I used Quilt Pro for Mac for design.

For the large patterns, I just cut the required shapes. For the next blocks, I made templates, and for the complicated blocks like the blue square, I used Quilt Pro and paper pieced. Each Brillouin zone is represented by a different fabric. Léon Nicolas Brillouin (d. 1969), a French physicist, made significant contributions to information theory, solid state physics, and other fields.

FIBONACCI 2

47” x 31”

Year Completed: 2014

Made by: Vaughn Nelson

Quilted by: Alisha Nelson Miller, Kennewick, WA

The Fibonacci sequence is formed by adding the previous two numbers, starting with 1: 1, 1, 2, 3, 5, 8, 13 and so on. Leonardo Fibonacci (d. 1250 in Pisa, Italy), who determined the sequencing, studied Arabic and Indian mathematics.

In this quilt, Dr. Nelson used EE Schenck ombre Gellato fabric cut into 2.5-inch strips. Lighter color fabric was cut to the lengths of the Fibonacci sequence, then separated by the dark fabric. Note that the top uses the reverse lengths described in the Fibonacci sequence.

GOLDEN SPIRAL

29” x 44”

Year Completed: 2014

Made by: Vaughn Nelson

Quilted by: Alisha Nelson Miller, Kennewick, WA

An approximation of the mathematical Golden Spiral uses squares with sides based on the Fibonacci sequence. In each step, a square the length of the rectangle's longest side is added to the rectangle. Then, an arc is formed from two opposing corners, which then forms the golden spiral.

Many plants grow new structures within such a spiral, resulting in patterns that we find pleasing if not beautiful. Golden Spiral was started with two 2-inch squares, using EE Schenck ombre Gellato fabric. Then a strip for the Golden Spiral was appliquéd, and the quilt was finished with long-arm stitching in intersecting spirals.

SINE WAVE

64” x 94”

Year Completed: 2011

Made by: Vaughn Nelson

Quilted by: Alisha Nelson Miller, Kennewick, WA

Trigonometry is the study of the relationship between the lengths of the sides and angles of triangles. The angles total 180 degrees, and for a right triangle (having one angle of 90 degrees), the ratios of the sides are constant. The sine function in trigonometry has an up-and-down curve that repeats every 360 degrees.

For this quilt, Dr. Nelson used two jelly rolls of Stonehenge fabric (typically 2.5 x 42-inch strips). He sewed the strips together and then cut across them in 2.5-inch strips. After plotting a sine wave, he determined the amount of shift translation to the left or right as he completed the pattern.

2 - 10

<

>

Website maintained by Quintessential Quilt Media. No portion may be reproduced without the written permission of the Texas Quilt Museum. Website design by Hunter-McMain, Inc. All Rights Reserved.