Following the White Rabbit: Torus Blossoms and Arithmetic Spirals in a Wonderland Inspired Vase

 I have some thrilling news to share! A few months ago, I received an email from  the American Mathematical Society asking to include my artwork,  Torus Blossoms in a Sliceform Vase in their 2027 Calendar of Mathematical Imagery. I immediately said yes.

While that honor was a milestone on its own, a beautiful coincidence recently brought everything full circle. I just watched my granddaughter perform as a colorful parrot in a ballet production of Alice in Wonderland at Towson University. It struck me right then: Lewis Carroll was the pen name of Charles Dodgson, a mathematician. Suddenly, the threads of mathematics, art, and family all connected into something magical. Inspired by that moment, I created this Wonderland-themed vase.

 Torus Blossoms and Arithmetic Spirals in a Wonderland Inspired Vase

The hexagonal vase features six panels, each depicting a scene from Wonderland's mystical forest. The beloved characters of Alice, the Mad Hatter, the White Rabbit, and the Cheshire Cat appear among enchanting woodland scenes. Perched in one of the trees is a colorful parrot, a small tribute to my granddaughter's role in the ballet. 

The panels and flowers look beautiful on every side.

Alice and the White Rabbit

The parrot and an enchanted mushroom

The Cheshire Cat and the Mad Hatter

The bouquet combines several torus blossoms, including some from the arrangement that will appear in the AMS 2027 Calendar of Mathematical Imagery, together with a new pointed torus blossom added to my growing collection.

The new torus blossom

The remaining flowers are based on arithmetic spirals coded in TurtleStitch. With each turn, the distance traveled gradually increases, producing elegant spiral forms that transform beautifully into paper blossoms. You can read more about their design, coding, and assembly in this earlier post.

The arithmetic spiral was rolled into a circle to produce a beautiful bloom at the top right.

If this Wonderland-inspired project has sparked your imagination, here are the instructions for creating your own mystical vase.

The Design

This project builds upon the hexagonal vase design I shared in an earlier blog posting (you can find the original tutorial here). The six-sided structure provides the perfect canvas for the mystical forest.

Add a multicolored LED tea light in the center for a magical glow. It makes a wonderful centerpiece or a cozy accent for any room in your home.

Materials You'll Need

• Neenah 65 lb Metallic White Pearl cardstock from Office Depot for the panels
• 65 lb green cardstock for the stems
• Vellum for backing the panels
• Battery-operated LED tea light (optional)

Cut Files

You'll need an electronic cutting machine to create this project:

• Silhouette users: Download the .Studio file [link to file]

• Cricut users: Download the SVG file [link to file]

Note: The SVG file extends beyond the initial viewable area. Simply zoom out to see the complete design.

Assembly Instructions

• Follow the assembly directions from the hexagonal vase project to construct your base structure
• Place your battery-operated LED tea light inside

Your Wonderland Awaits

Funny how life weaves unexpected connections together. An email from the AMS, a ballet performance, Lewis Carroll's mathematical imagination, and a new paper vase all converged to inspire this project.

Follow the White Rabbit...your own Wonderland adventure awaits.