Flow Field: Tempest — Flow Fields mathematical physical art

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Flow Field: Tempest

Flow Fields

Alternating sources and sinks — streamlines flow from positive poles to negative ones, like magnetic field lines between seven dipole pairs.

Price

$29.00

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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
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The mathematics

About this system

A flow field assigns a direction to every point in the plane. A particle dropped into the field traces a curve that always follows the local arrow. Build the field from smoothly varying noise (Perlin, simplex, or layered sinusoids) and thousands of trajectories braid into curtains, vortices, and rivers without ever crossing. This image is the result of thousands of particles released into one specific mathematical field, each particle leaving a continuous trail.

In the Flow Fields collection

A flow field assigns to every point in the plane a direction — and a particle dropped into the field will trace a curve that always follows the local arrow. Build the field from smoothly varying noise (Perlin, simplex, or layered sinusoids) and the resulting trajectories braid into curtains, vortices, and rivers without ever crossing. The technique sits at the boundary of generative art and computational fluid dynamics. Each image in this collection is the result of thousands of particles released into a fixed mathematical field, each one rendered as a continuous trail. The animations show the same fields evolving slowly in time, so that the entire flow pattern breathes while maintaining its underlying structure.

∂x/∂t = cos(N(x,y)), ∂y/∂t = sin(N(x,y)), N = Σ aₖ sin(fₖ·r + φₖ)