The Artwork in More Detail

This artwork is part of the series Reality and Imagination: Digital images created with custom code, based on the complex function 1/z. The idea is to find beauty and inspiration in the bare essence of mathematics! Seemingly simple mathematical concepts sparkle and glitter, if viewed from the right vantage point.

Real and imaginary parts of the complex function 1/z are envisaged as a cityscape or a space station: Two towers are floating through empty space. Infinitely elongated bells.

In a series of images, these virtual structures are shown from different viewing angles. The contour lines of these two functions are perfect circles – rings which are aligned along the circumference. Stacking these rings gives rise to tower-like structures. Gold is the color of reality; Blue is the color of imagination.

Elke Stangl’s (elkement) artworks related to functions over the complex plane had originally been inspired by Roger Penrose’s book The Road to Reality. Penrose introduced complex functions as fundamental building blocks of mathematics used in theoretical physics. His engaging examples of the “magic of complex numbers” let elkement explore these functions: First with mathematics software SageMath, then using javascript and the framework three.js.

The asymmetric towers lean on each other, and they intersect each other. They meet in the vertical line erected at the zero point. x and -y are π/2 apart, speaking of them in terms of the complex plane. These towers can be rotated into each other. They chase each other, one lagging by π/2, like current and voltage in a resonant circuit, like force and amplitude of an oscillation.

If z is expressed as x + iy, real and imaginary parts of 1/z are obtained by multiplying nominator and denominator by x – iy. Moving away from the zero point, x² + y² in the denominator finally wins, and both parts become zero. Denominators are x for the real part and -y for the imaginary part. At the zero point, the denominator goes to zero faster than the nominators, thus both parts have poles. As x and -y change sign when the zero point is crossed, each function is made up of two infinite towers, one extending to infinity, the other to minus infinity.

The image is a scientific visualization of sorts: Contour lines have been promoted to metallic tubes to make the structures both ethereal and solid, and the viewpoint has been chosen to make it more enigmatic than educational. It is an invitation to ponder about the mathematics of complex functions, but it should also speak to viewers who are not familiar with the underlying concepts

A page dedicated to the series Reality and Imagination: https://elkement.art/reality-and-imagination/

Related Links

Learn more about complex analysis on Wikipedia.

The Artwork in More Detail

3-dimensional.space is joint work by Rémi Coulon, Sabetta Matsumoto, Henry Segerman, and Steve Trettel to render accurate images of the eight Thurston geometries and their quotients. We make this software accessible to explore and encourage you to visit our website that hosts various demonstrations we have created along the way, as well as tutorials and documentation for the codes.

Related Links

Learn more about Non-Euclidean geometry on Wikipedia.

Explore these geometries on your own: 3-dimensional.space.

The Artwork in More Detail

The starting point is a row of real numbers, x_n, that decrease incrementally and a column of imaginary numbers, y_n, that increase incrementally.  A starting grid is created by applying a complex formula to each row/column combination z (= x_n+iy_n). 

For Forces, Web and Pearls, the starting grid formula was a polynomial [1-z^a]^b. For PMax, the starting grid formula was Ln[z].

The formulas applied to create each iteration were chosen to result in a variety of interesting patterns, and usually involved varying the formulas used for each iteration.

Forces started with 4-3i times a complex power 11+.1i that alternated to -12-.05i each iteration except for Iteration 3, which was the complex tangent of Iteration 2.

Web alternated the complex tangent with the complex natural logarithm, with the exception of Iteration 5, which was Iteration 4 raised to the power of negative 12.

Pearls alternated the complex exponential, (e^z), with the complex natural logarithm for the first five iterations, then used -i times a complex power which alternated each iteration between -13-.2i and 13+.2i.

PMax used the complex power -21-.1i for all iterations.

For visualizing the final grid of absolute values, I used Excel’s conditional formatting setting that assigns 3 different colors based on the percentile of numeric results. I used percentile rather than percent or number because it colors each pixel according to their value relative to the other values in the grid. The choice of percentiles and colors involved trial and error as to what looked most interesting.

Related Links

Learn more about Complex numbers and Complex Analysis on Wikipedia.

The Artwork in More Detail

From the mathematician’s perspective:

In mathematics, the notions of “integer partition” and “triangular number” are well known concepts. We were inspired by a specific interpretation of the notion of “triangular partition” – one that is totally distinct from the more standard definition of a triangular partition that has gained recent popularity. The more standard definition of a triangular partition in mathematics is a partition whose Ferrer diagram is “cut off” by a straight line (see link below). This is not the notion of triangular partition that inspired this work. Instead, we interpret a triangular partition as a partition of a triangular number (whose dots are arranged into an equilateral triangle) up to the natural symmetries (rotations and reflections) of the triangle. In general, there are more of these objects than plain old partitions. It is very interesting to try to calculate the number of these  “triangular partitions” for a given triangular number.

From the artist’s perspective:

My interest in mathematical art stems from a series of inspiring conversations I have had with an art-curious friend and colleague, mathematician Dan Rowe.  Dan has been teaching me about mathematical concepts that are potentially applicable to the visual arts, including “triangular partitions.”  For Abiogenesis I selected, from an array of differently partitioned 15-dot equilateral triangles, configurations that seem visually interesting.  These I combine and overlap in double-sided paintings using pigmented acrylic medium on a transparent film called DuraLar. Though I sometimes end up warping the partitions, it is still possible to identify the discrete triangles, especially when there’s a grid of dots in the background, as in Abiogenesis. The partitions serve as an organizing principle, imparting to these abstract paintings an underlying order that is not overly fixed or rigid, but flexible and variable.

Related Links

Learn more about Integer partitions and triangular numbers on Wikipedia.

Here is an interesting alternate definition of a triangular partition: https://arxiv.org/pdf/2203.15942

An expanded description of the artwork

Fractals are self-similar geometric shapes that display amazing details on all scales. Their fascinating beauty reveals a wealth of detail upon successive magnifications. The term “fractal” was coined by the famous mathematician Benoit Mandelbrot in 1975. With the help of powerful modern computer technology, fractals were extensively explored by mathematicians, computer scientists, and artists ever since. My “Dreamland Fields” image was created while exploring the depths of the 5th order Newton/Mandelbrot set fractal. It consisted by navigating through numerous regions of that particular fractal landscape, as well as using various magnification factors until this beautiful dreamlike composition was brought into existence.

The famous simple equation for the Mandelbrot fractal (Z_n+1 = Z_n² + c) generates an infinite number of complex and mesmerizing images. There are many fractal-generating tools available in today’s techno-world for all curious art and mathematics loving minds to enjoy, and create mathematical beauties the magical universe of fractals offers and makes our hearts sing.

Related Links

Learn more about the Mandelbrot set on Wikipedia.

The Artwork in More Detail

Near the end of his life, the British mathematician Alan Turing proposed a groundbreaking mechanism for the formation of spatial patterns in nature, known as morphogenesis. This occurs when two or more chemicals react in just the right way while diffusing through a substrate, resulting in formations now referred to as Turing patterns.

For nearly fifteen years, I have explored Turing patterns in my abstract artwork. The reaction-diffusion process Turing proposed can be simulated in various ways, and my approach often involves repeatedly blurring and sharpening an initial seed image until a stable pattern emerges. Sometimes I work with image editing software like Adobe Photoshop, but for the Symmetry Series, I developed custom Python software to handle this process.

Each piece in this series begins with a random grayscale image, which I mathematically “fold” to create horizontal and vertical symmetry. The software then repeatedly applies blurring and sharpening, simulating Turing’s reaction-diffusion process until a stable pattern is achieved.

Once I find a pattern that resonates aesthetically, I use it as the foundation for a painting. The Turing pattern becomes the underpainting, onto which I layer thousands of hand-painted marks in acrylic, working with carefully mixed color gradients. My goal is to create a dynamic visual experience where the viewer is continually drawn in, discovering new elements from different angles, distances, and lighting conditions.

Andrew Werth wrote an article and gave a presentation about Turing patterns in Photoshop for the Bridges conference in 2015.

Related Links

Learn more about Turing patterns on Wikipedia.

The Artwork in More Detail

For this work, the location of each circle in the plane is determined by plotting the path of all the results of the sequence for a given input, translating the graph accordingly and rotating it a little clockwise if even and counterclockwise if odd. This rotation is just to make the graph look “less” cluttered and doesn’t really have much to do with the Collatz conjecture other than using the intermediate d value’s oddness or evenness for the angle of rotation, which is constant.

Example: the initial value n is 1. 1 is odd, so multiply by 3 and add 1. Result is 4. The program translates up 4 from the lower left corner (the origin) and rotates a small angle clockwise. Since 4 is even, divide 4 by 2. Result is 2. The program translates up 2, and rotates a small angle clockwise. This process continues until the sequence produces a 1. At that point, where ever it may be, the program plots a circle. The number of steps the program takes to converge to 1 is used to determine the circle’s radius.

Then, the program moves to the next whole number 2 and repeats. Each new “path” starts from the lower left hand corner. This program tests all the integers up to 10,000.

So, in summary, the radius of each circle is the equal to the number of steps it takes for the sequence to converge to a 1, and the location in the plane is a result of all the rotations and the “length” of the path until the function converges to 1.

The color palette I used pretty much just cycles though ten possible colors.

Related Links

Learn more about the Collatz Conjecture on Wikipedia.

The Simple Math Problem We Still Can’t Solve in Quanta Magazine

The Artwork in More Detail

Mathematics is often a combination of hard work and happenstance. So is art.

I use mathematics, principally geometry, as a source of inspiration for my work. The actual mathematical description of events is a process of discovery of Nature and the world we live in. Like landscape painters, while it may seem odd at first, I consider myself a painter of Nature and the hidden elements that compose it because all my work is based on solid, provable phenomena discovered first by mathematicians.

* Minimal surfaces for example: in the late 1800s, physicist J. Plateau1 found that soap bubbles characterized minimal surfaces best. This keen observation of a problem mathematicians have been studying since antiquity is not inconsequential. These elegant and complex shapes found in Nature from butterflies, beetles, or black holes are studied today in statistics, material sciences, molecular engineering, and architecture.

In a 52-illustration project from which Sphere Eversion is extracted, I entrusted mathematicians to provide me with an accurate description of the many surfaces they discovered to explore the visual and poetic aspects of these intriguing forms.

A sphere eversion is a way to evert a sphere is to turn it inside-out by means of a continuous deformation. It allows the surface to pass through itself.  Blind mathematician Bernard Morin demonstrated that an eversion based on a Morin surface halfway model has the minimum possible number of topological events. The University of Illinois hosts John Sullivan’s extended paper on this topic: John Sullivan (1999). A History of Sphere Eversions. https://www.mi.sanu.ac.rs/vismath/sullivan/opt2.htm

* Excerpt from the book Minimal Surfaces, The Math-Art series, volume 13.

Related Links

Learn more about sphere eversions on Wikipedia.

The Artwork in More Detail

This piece was created by assembling four transformations of the same three-dimensional parametric curve, which are the same form observed at different moments in time. The equations that generate the curves involve simple trigonometric functions that have gained a complex form by introducing parameters that are carefully adjusted by hand.

The four curves have been aligned into two pairs of curves in opposition, appearing to pull apart as in the biological process of mitosis.

This symmetric scene exists statically in space with curves that do not overlap but come together to form a single piece that projects a feeling of movement. The animation presented here is an exploration of the static scene from the viewpoint of a camera maneuvering around the curves through space.

Related Links

Learn more about parametric equations on Wikipedia.

Learn more about IanniX, a graphical open source sequencer, based on the works of Iannis Xenakis.

The Artwork in More Detail

A combination of Experimental Mathematics and Visual Art

Experimental mathematics is a unique approach that combines computation, intuition, and formal proof. It emphasizes the use of computational tools, visualization, and numerical experiments to explore mathematical phenomena, uncover patterns, and develop conjectures. As Kurt Gödel once noted, if mathematics describes an objective reality, inductive methods, similar to those used in physics, can also be applied in mathematics. Jacques Hadamard echoed this sentiment, asserting that mathematical rigor serves to validate the insights gained through intuition.

In this spirit, experimental mathematics becomes a powerful tool for fostering intuition and discovery. It plays a crucial role in mathematics education by allowing direct engagement with mathematical objects, helping to develop deeper understanding.

My exploration in this field often involves writing Python code in Jupyter notebooks, which provide a robust platform for numerical computation, data manipulation, and advanced visualization.

The central question of the “Eigenfish” series is: how are the eigenvalues distributed in the complex plane when two matrix elements are treated as real parameters, t₁​ and t₂, and allowed to vary?

An elegant theorem known as the Gershgorin circle theorem describes a region in the complex plane that contains all the eigenvalues of a square matrix. These regions, composed of circles, are straightforward to compute and visualize. However, my work extends this by computing and visualizing eigenvalues through Python, using NumPy and Matplotlib.

The resulting images depict eigenvalues in the complex plane for matrices with elements drawn from the set {0, -i, i, 1, 1/2}, with 2,000,000 random samples of t₁ and t₂​ within the range [-20, 20]. The parameters are randomly selected, and while the insights gained from this visualization are uncertain, the result is undeniably a striking piece of mathematical art.

This blend of experimental mathematics and visual art showcases the beauty of mathematical exploration, where the process of discovery is as significant as the final result.

Concept and Process

At the core of this project is the Eigenfish class, a custom Python class designed to generate and manipulate matrices, with a particular focus on their eigenvalues. Here’s a breakdown of the process:

1. Matrix Structure: The foundation of each eigenfish is a square matrix. Specific elements within this matrix are designated as variables, represented by parameters t₁,t₂,…,t_n. These parameters can be adjusted, leading to a dynamic matrix that changes with each iteration.
2. Parameter Sampling:
   • • Rectangular Distribution: Parameters t₁,t₂,…,t_n are sampled from a uniform distribution within a defined range [−r, r], or from a normal distribution with a specified standard deviation. These distributions create varying eigenvalue patterns depending on the range or spread of the sampling.
     • Torus Distribution: Alternatively, parameters can be sampled uniformly from a toroidal surface, producing eigenvalue patterns with a circular symmetry, reflecting the periodic nature of the torus.
3. Eigenvalue Calculation: For each sampled set of parameters, the eigenvalues of the matrix are computed. These eigenvalues are the roots of the characteristic polynomial of the matrix and can be visualized in the complex plane.
4. Visual Representation: The calculated eigenvalues are plotted, often in the complex plane. The collection of these points forms the visual art piece, with patterns emerging based on the distribution and behavior of the eigenvalues.

Eigenfish art invites viewers to appreciate the inherent beauty of mathematical structures, transforming the intricate relationships of matrices and their eigenvalues into visual art that is both intriguing and intellectually stimulating.

Simone Conradi has written an article about the artwork Eigenfish: https://doi.org/10.57037/b-imi.00104.1mas400

Related Links

Learn more about eigenvalues on Wikipedia.

The Artwork in More Detail

Interlace patterns are found in ancient Roman, Celtic and Islamic art. One way to design an interlace pattern is to first draw the underlying graph (or network), and then weave the ribbons of the design around this frame. By following a simple procedure, the interlace pattern corresponding to the graph reveals itself. Usually the frame is then removed so that it is not visible in the final design.

The frame for this interlace pattern is related to the Sierpiński triangle, which is a beautiful mathematical object created using recursion. Starting from an equilateral triangle, join the midpoints of each edge in pairs using straight lines. This partitions the original triangle into four smaller triangles, with the middle triangle upside-down.  Remove this upside-down triangle, leaving three smaller triangles behind. This is the end of step 1 of the recursion. Now repeat this process on these three smaller triangles, removing three even smaller upside-down triangles: this completes step 2 of the recursion.  Keep going as many times as you like to create an intricate, self-similar pattern of triangles.

To create the frame for this piece, I put a twist on the Sierpiński triangle construction by stopping at different levels of recursion in different parts of the design. This led to a kind of multiscale effect that I found interesting. When I added the interlace ribbons to this frame, many circles naturally arose at these different scales.

In knot theory, a knot consists of one continuous strand, while more than one intertwined strand is called a “link”. So I called this piece Sierpiński Links.

Related Links

Learn more about the Sierpiński triangle and knot theory on Wikipedia.

The Artwork in More Detail

This piece is an Abelian Sandpile, a cellular automaton that simulates the movement of virtual grains of sand. The Abelian Sandpile model was first described by physicists Per Bak, Chao Tang, and Kurt Wiesenfeld to illustrate how natural systems can self-organize into a critical state (like an avalanche) without needing the trigger of a catastrophic event.

In a typical sandpile, sand is added randomly throughout the grid, or in large quantities in a few cells. Each cell that contains four grains of sand or more is toppled, moving an equal quantity of sand grains to its four Von Neuman neighbors (the four cells directly adjacent to the current cell). Toppling is an abelian operation because the order in which cells are toppled does not affect the resulting sandpile. This process repeats until all cells contain three grains of sand or less at which point the sandpile has stabilized. Cells are then colored according to the number of grains they contain, producing a fractal-like pattern.

The sandpile in this artwork was generated on a regular grid, 3201 × 3201 cells in size, with a uniform seed of two grains of sand per cell. An additional 3.2 million grains of sand were distributed evenly between four drop-spots at an equal distance from the center of the grid. The sandpile was then toppled and stabilized using the process described above.

Before coloring the stabilized pile, I applied a process that “eroded” the sand further. Each cell was checked simultaneously to see if it had at least two Von Neuman neighbors that contained three grains of sand. If it did not, one grain was removed from that cell (and the entire sandpile). I repeated this process for three iterations. This had the effect of removing noise and sharpening the detail of the remaining features. I did this to further simulate natural processes, treating the sandpile not as a fixed object, but something affected by the passage of time and the elements.

Cells containing 0 grains of sand are colored black, 1 grain light blue, 2 grains purple, and 3 grains tan. Colors were selected to increase contrast and for aesthetic appeal.

Related Links

Learn more about the Abelian sandpile model on Wikipedia.

The Artwork in More Detail

Of Time and Cosmos is a fusion of visual art and poetry, born from a deep exploration of mathematical concepts and personal reflection. Over the course of 31 days, I engaged with a list of mathematical terms from Mathober 2022, each serving as a prompt for daily creation. Each day involved researching the meaning of the word, contemplating its implications, and then translating those insights into a unique work of art accompanied by a meditative haiku.

The artworks take place in cosmic landscapes and incorporate intricate geometric forms. Each piece interweaves abstract mathematical ideas with the natural world and human experience. Themes such as balance, motion, infinity, and interconnectedness are expressed through a variety of visual metaphors. The paired haikus complement the visuals, distilling the essence of each mathematical concept into concise, reflective verse.

This project is a journey through curiosity, self-discovery, and the beauty of both the finite and infinite.

Read the entire book featuring 31 images and 31 haikus: Of Time and Cosmos

Related Links

Learn more about category theory on Wikipedia.

The Artwork in More Detail

The basic sphericon consists of two half elements. The novelty in my design is that I increased the number of elements to six. During the formal experiments, I noticed that a new sphericon can even be created from two different-shaped elements. Later, I increased both the number of basic elements and the number of shapes. The number of variations is enormous.

In the metamorphosis video, a centrally symmetric solid can be seen, but it is also possible to create asymmetric sphericons from multiple elements. I would like to mention the concept of tessellation here, as the sphericon always starts from a base plate, which can also be asymmetric. This base plate is covered with symmetrical plane figures in the case of multiple elements, from which I derive half solids of revolution. The outer elements will share surfaces with those on the opposite side. The sphericon shown in the video is topologically a torus; the two elements have the same volume. 

Related Links

Learn more about sphericons on Wikipedia.

Related Links

Learn more about Hexastix on Wikipedia.

The Artwork in More Detail

These animation was generated by cohomology_fractals, a web application written in Javascript and GLSL. It uses the local GPU to render cohomology fractals in real-time. To navigate, use the arrow and WASD keys. Also, you can change the manifold and cohomology class using the dropdown menu.

Learn more about the construction of these images, watch our explanation video or read our article from Bridges 2020.

Related Links

Learn more about cohomology on Wikipedia.

The Artwork in More Detail

Morse theory, established by Marston Morse in the late 1920s and now part of differential topology, describes how to build possibly-complicated objects known as “smooth manifolds” from simple standard pieces.

The prototypical example is a torus, the abstract surface of a doughnut. To make a 21st century analogy, imagine a torus leaning on edge inside a 3D printer. What do we see in a time-lapse movie of the printing process? At each time, what portion of the torus is present, and what curve(s) does the print head trace?

Initially, we see a shallow bowl, and the print head traces a single closed path. When the print reaches the bottom of the hole in the middle, something changes: the print head traces one figure-8 (note the X-shaped region toward the right side about one-third of the way up), then starts to trace two closed paths. This continues until the print reaches the top of the hole, where the two loops merge into another figure-8. After this, the print head traces a single loop, which shrinks to a point at the top.

Generally, the cross sections change precisely where a horizontal cutting plane is tangent to the torus. Morse theory details these qualitative changes for smooth manifolds of arbitrary dimension.

“Morse Theory, Oblique” depicts a torus sliced into bands and gaps. The bands’ coloration grades from warm, subterranean gold through a shadowed earth green to bright celestial aqua, suggesting rising, emergence, and completion.

Related Links

Learn more about Morse Theory on Wikipedia.

Related Links

Learn more about Conway’s Game of Life.

Learn more about the mathematics of a Rubix’s Cube.

The Artwork in More Detail

I heard about the torus knot for the first time at the end of August 2019, and fell in love with the rules behind it. The key is how many knots there are and how the knots are tied, not the parametric equations that define it. I started from the geometric structure and explored various combinations using Rhino software. I also defined a symbol T(m, n) whose relationship with p and q is:

T(m,n) ~ d x (p,q), where m = d x q, n = d x p, and d=gcd(m,n). When m and n are relatively prime, T(m, n)=(q,p). 

When m and n are relatively prime, the torus knot is a cycle. When m and n are not relatively prime, such as in T(12, 8), there are four copies of (2,3).

The pictures is the envelope of T(5,3). The work in the video is the envelope of T(4,3) rotated by an angle relative to the tangent plane. They are all full of dynamic beauty.

How do I think about the envelope? Imagine the trajectory formed by all the droplets (real objects that look like “points”) on the curve when they are thrown along the curve at the same time. Oh! How beautiful the picture is. 

After all, mathematics deals with facts, and art focuses on opinions. When the two meet, it is full of fun.

Experience a video about these objects produced by the artist.

Related Links

Learn more about torus knots, a tangent lines to a curve, and an envelope of a curve on Wikipedia.

Related Links

Learn more about space-filling curves on Wikipedia.

The Artwork in More Detail

One way to think about what’s going on is that the group G={diag(eᵗ, e⁻ᵗ)} of 2 × 2 diagonal matrices of determinant 1 is acting on the plane. This action is pretty much the simplest possible action which motivates the notion of a Geometric Invariant Theory (GIT) quotient: if this group acts on points of the form (x,y), then the product xy is conserved, so each nonzero number λ corresponds to an orbit which is just the hyperbola xy=λ. However, there are three different orbits for which xy=0, namely the two axes (with the origin removed) and the origin itself. Unfortunately, the closures of these three orbits intersect, so the orbit space is non−Hausdorff unless we do something slightly more sophisticated. In GIT, the upshot is to identify the three orbits and then the orbit space is just a copy of the line.

However, there’s rather more going on in the visualization. If we think of a lattice Λ in the plane ℝ², then we can think of G as acting on Λ. Of course, this will generally change the lattice, but if we choose the lattice very carefully, we can get a periodic action: after some finite time t₀, the lattice comes back to itself (even though the individual points have of course moved, and always end up shooting off to infinity). This is the modular flow.

This work was partially supported by the National Science Foundation (DMS–2107700).

Related Links

Modular flow introduction by Bruce Bartlett: https://golem.ph.utexas.edu/category/2014/04/the_modular_flow_on_the_space.html

Animation source code (with descriptions): https://github.com/shonkwiler/geometry-in-motion/blob/main/source/flow.nb
Source code in a viewable format: https://community.wolfram.com/groups/-/m/t/3061781

The Artwork in More Detail

Here is an illustration about how the harmonograph draws lissajous curves. 

The laser I use uses a device galled a XY galvo scanner with two rotating actuators that steer the angle of the laser beam in two directions. When I steer a sine wave to the rotating mirrors, the signal very much resembles natural oscilations from a pendulum.

Related Links

Learn more about Lissajous curves, the harmonograph, and cyanotypes on Wikipedia.

Here is a PDF that describes the mathematics of a harmonograph.

About the Curator

Christopher R. H. Hanusa is a Professor of Mathematics at Queens College. His mathematical research is in algebraic and enumerative combinatorics, most recently studying the combinatorics of flow polytopes. He is also a mathematical artist whose works are often generative in nature and draw on his varied mathematical interests. A key emphasis of his art is on the play between randomness and deliberation. His mathematical jewelry is in the gift shops at the National Museum of Mathematics and the Queens Museum and has been featured multiple times in the Math+Fashion show at the Bridges Conference.

Visit Christopher Hanusa’s portfolio on the web at christopherhanusa.com and follow him on social media at @mathzorro: (bluesky) (instagram).

Institutions interested in partnering with Queens College to host this exhibition on their local displays should contact Prof. Christopher Hanusa (he/him) at chanusa (at) qc.cuny.edu.

Can’t wait to experience more Mathematical Art?

View the Exhibitions from the Bridges Organization, featuring connections between mathematics and art, music, architecture, and culture.
Attend the monthly chats and presentations by the Illustrating Mathematics community.
Read the articles in the Journal of Mathematics and the Arts.