Rose Verdant — Radial Symmetry mathematical physical art

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Rose Verdant

Radial Symmetry

A botanical radial study in jade and pale mineral green.

Price

$29.00

Shipping calculated at checkout

Format Art Print
Size 18 × 24 in
Material Enhanced matte paper · 200gsm · archival · unframed
Resolution 300 DPI · rendered at 5400 × 7200 px
Production Professional print-on-demand · ships from nearest facility
Shipping Most countries · calculated at checkout
Shipping & Delivery ⌄

Each print is produced and shipped from the nearest facility in our global print network. Production normally takes 2–5 business days, then shipping follows Printful's live estimate for the destination. The ranges below are current standard-rate estimates and can vary by exact address, product, and carrier availability.

Standard US 3–6 days · EU 3–15 days · Asia/Pacific 2–17 days · LatAm 5–25 days
Express Availability varies by product and destination
RegionCountriesEst. delivery
United States All 50 states + territories 3 – 6 business days
United Kingdom UK 2 – 11 business days
Canada Canada 2 – 10 business days
Australia Australia, New Zealand 3 – 17 business days
European Union Germany, France, Spain, Italy, Netherlands, Belgium, Austria, Sweden, Poland, Denmark, Finland, Ireland, Portugal, Czech Republic, Romania, Greece + more 3 – 15 business days
Norway & Switzerland NO, CH 3 – 15 business days
Latin America Brazil, Mexico, Chile, Colombia, Argentina, Peru + more 5 – 25 business days
Asia Pacific Japan, South Korea, Singapore, India, China, Hong Kong, Taiwan, Malaysia, Thailand, Philippines + more 2 – 20 business days
Middle East UAE, Saudi Arabia, Israel 5 – 20 business days
Rest of world Most supported countries and territories 5 – 25 business days

Note: Delivery times are estimates and not guaranteed. Exact rates are confirmed at checkout with Printful live shipping data. Shipping is unavailable for Russia, Belarus, Cuba, Iran, North Korea, and Syria.

Shipped worldwide · professionally printed and fulfilled

The mathematics

About this system

Rose curves are defined in polar coordinates by r = a·cos(kθ) or r = a·sin(kθ). When k is an integer, the curve has k petals if k is odd, and 2k petals if k is even — a delightful number-theoretic surprise. When k is irrational, the petals never close and the curve fills the disk with a dense quasi-periodic pattern. This image is the literal locus of a single polar equation, traced as a continuous mathematical object.

In the Radial Symmetry collection

Polar coordinates collapse two-dimensional geometry to two simple ideas: a distance from the center and an angle around it. From this minimal starting point you can grow elaborate symmetric forms. The rose curves r = a·cos(kθ) trace petal patterns whose count depends on whether k is even or odd. The superformula of Johan Gielis generalizes this further with six parameters, producing flowers, stars, leaves, and shells from a single closed-form expression. The result is geometry that recalls nature without imitating it — the same mathematics that describes radiolaria, snowflakes, and pollen grains. Every form in this collection is the literal locus of a polar equation, rendered as a continuous mathematical object.

r(theta) = a cos(k theta), r(phi) = (|cos(m phi / 4)|^n2 + |sin(m phi / 4)|^n3)^(-1 / n1)