Physarum
Grow branching networks with a Physarum-style agent model and print them. Thousands of agents move over a grid of trail values: each one looks ahead with three sensors, turns towards the strongest trail, steps forward and adds to the trail where it lands; then the whole trail spreads to its neighbours and fades a little. The paths reinforce each other into a network. The model follows the one in Jeff Jones’s 2010 paper on approximations of Physarum transport networks. Set up to 50,000 agents on a grid of 32 to 400 cells each way whose edges wrap round, the sensor angle and distance, the turn angle, the step, the deposit and the decay, the start and the seed, and up to 3,000 steps. Draw the trail as two-tone cells, shades or contour lines, repeat the seamless tile, and download a PDF, a 300 DPI PNG or an SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). Real size prints on one sheet when the drawing fits; the check bar in the footer lets you confirm the scale. The SVG holds the drawing at the printed size.
Agents
Look
Page
Runs in your browser with our own code: nothing you type is uploaded or saved. Every agent move and every trail update is worked out by our own code on the grid shown. You may use what you make here, including commercially, with no credit needed.
How to grow and print a physarum-style network
- Pick a preset, or set the grid and the number of agents.
- Set the sensor angle and distance, the turn angle, the step, the deposit and the decay.
- Choose the start, the seed and the number of steps, and wait for the preview (long runs show their progress).
- Choose two-tone cells, shades or contour lines, the threshold, the colour and the tile repeat; choose Fitted to one page or Real size and the paper.
- Download the PDF and print at 100% (Actual size), or the PNG or SVG.
What you can use it for
- Generative art posters of branching networks
- Seamless pattern tiles for fabric, wrapping paper and backgrounds
- Plotter, laser and vinyl art from the contour SVG
- Lessons on agent-based models and emergent patterns
- Textures for games and 3-D work
- Comparing sensor and turn settings side by side
The 16 presets
| Preset | Agents | Grid | Steps | Sensor angle / distance | Turn | Decay | Start | Dark | Look |
|---|---|---|---|---|---|---|---|---|---|
| Network: 12,000 agents, 120 steps, sensor angle 22.5°, turn 45°, sensor distance 9 | 12,000 | 200 × 200 | 120 | 22.5° / 9 | 45° | 0.1 | random | 15.8% | two-tone cells |
| Young network: 60 steps (many thin strands) | 12,000 | 200 × 200 | 60 | 22.5° / 9 | 45° | 0.1 | random | 26.6% | two-tone cells |
| Older network: 600 steps (fewer, thicker strands) | 8,000 | 200 × 200 | 600 | 22.5° / 9 | 45° | 0.1 | random | 5.4% | two-tone cells |
| Sensor distance 5 | 12,000 | 200 × 200 | 120 | 22.5° / 5 | 45° | 0.1 | random | 14.3% | two-tone cells |
| Sensor distance 20 | 12,000 | 200 × 200 | 120 | 22.5° / 20 | 45° | 0.1 | random | 18.7% | two-tone cells |
| Sensor angle 11.25°, turn 22.5° | 12,000 | 200 × 200 | 120 | 11.25° / 9 | 22.5° | 0.1 | random | 16.5% | two-tone cells |
| Sensor angle 45°, turn 45° | 12,000 | 200 × 200 | 120 | 45° / 9 | 45° | 0.1 | random | 14.4% | two-tone cells |
| Start in a disc: 15,000 agents | 15,000 | 200 × 200 | 120 | 22.5° / 9 | 45° | 0.1 | disc | 4% | two-tone cells |
| Start on a ring, facing in: 10,000 agents | 10,000 | 200 × 200 | 150 | 22.5° / 9 | 45° | 0.1 | ring, facing in | 3.8% | two-tone cells |
| Dense: 30,000 agents on 300 × 300 | 30,000 | 300 × 300 | 100 | 22.5° / 9 | 45° | 0.1 | random | 16.6% | two-tone cells |
| Slow decay 0.03 | 12,000 | 200 × 200 | 120 | 22.5° / 9 | 45° | 0.03 | random | 23.7% | two-tone cells |
| Network as contour lines | 12,000 | 200 × 200 | 120 | 22.5° / 9 | 45° | 0.1 | random | 14.5% | contour lines |
| Network in three shades | 12,000 | 200 × 200 | 120 | 22.5° / 9 | 45° | 0.1 | random | 19.7% | shades |
| Seamless tile repeated 2 × 2: 120 × 120 | 4,500 | 120 × 120 (× 2 × 2) | 120 | 22.5° / 9 | 45° | 0.1 | random | 15.5% | two-tone cells |
| Largest grid: 400 × 400, 40,000 agents, 100 steps | 40,000 | 400 × 400 | 100 | 22.5° / 9 | 45° | 0.1 | random | 17.2% | two-tone cells |
| Real size: 120 × 120 at 1.4 mm per cell | 4,500 | 120 × 120 | 120 | 22.5° / 9 | 45° | 0.1 | random | 17.4% | two-tone cells |
Step 1 and deposit 5 on every preset. Dark is worked out by the tool: the share of cells at or above the threshold (0.25 of the 99th-percentile cell unless the preset says otherwise).
Trail total, step by step
| Step | Total before | Total after | (before + 2,000 × 5) × 0.9 |
|---|---|---|---|
| 1 | 0.000 | 9000.000 | 9000.000 |
| 10 | 55132.156 | 58618.940 | 58618.940 |
| 50 | 89484.622 | 89536.160 | 89536.160 |
2,000 agents on 64 × 50, deposit 5, decay 0.1, worked out by the tool. The two right-hand columns agree on every step in our tests.
What prints
| Download | What is in it |
|---|---|
| The tile (or its repeats) fitted to one page or at real size, vector, with the settings, the trail total and a check bar | |
| PNG 300 DPI | The same sheet as a picture |
| SVG | The tile at the printed size: cells as exact rectangles, one path per colour, or the contour as one stroked path |
For a cutter that needs DXF, use SVG to DXF.
Which tool to use
| You want | Use |
|---|---|
| Networks grown by trail-following agents | Physarum (this page) |
| Paths of a flocking simulation | Boids |
| Contour lines of a height map | Topographic Map Generator |
| Cells split by nearest points | Voronoi Generator |
| Repeating geometric SVG tiles | SVG Pattern Generator |
Other tools: the Topographic Map Generator draws contour maps, the Voronoi Generator splits a page into cells and the SVG Pattern Generator makes repeating tiles.
More free tools
Patterns, textures and printables?
Drawing and print tools that run privately in your browser, with no sign-up and no watermark.
Frequently asked questions
What is a Physarum-style agent model?
A simulation in which many simple agents follow and lay down trails on a grid. Sage Jenson’s notes on the model (read 13 November 2026) describe it this way and cite Jeff Jones’s 2010 paper “Characteristics of pattern formation and evolution in approximations of Physarum transport networks”. This tool runs that kind of model with the settings you choose; it makes no claim about how any living organism behaves.
What does each agent do in a step?
It reads the trail under three sensors at the sensor distance ahead: straight on and at the sensor angle to the left and right. If straight on is the strongest it keeps its heading; if straight on is the weakest it turns left or right by the turn angle at random (from the seed); otherwise it turns by the turn angle towards the stronger side. Then it moves forward by the step, wrapping round the edges, and adds the deposit to the cell it lands on. Agents move one after another in a fixed order and may share a cell.
What happens to the trail?
After all agents have moved, every cell becomes the mean of itself and its 8 neighbours (3 × 3, wrapping round the edges), which keeps the total the same, and then every cell is multiplied by 1 minus the decay. So each step the total trail becomes (total + agents × deposit) × (1 − decay), and our tests check that sum exactly on every step.
How does the network change over time?
In our runs it starts as many thin strands and merges into fewer, thicker ones. The presets show it: Young network (60 steps) is dark on 26.6% of the grid; Network (120 steps) is dark on 15.8% of the grid; Older network (600 steps) is dark on 5.4% of the grid (worked out by the tool).
Why does it tile with no seam?
The grid’s left edge touches its right edge and its top touches its bottom: the sensors, the moves and the 3 × 3 mean all wrap round. Our tests show that the spreading step of a shifted map is the shifted result, bit for bit, and that every copy of a repeated tile is the same cell for cell.
What do the looks show?
The trail is divided by its 99th-percentile cell (and capped at 1), so a few very bright cells do not wash out the rest. Two-tone fills every cell at or above the threshold (or below it, with Swap dark and light). Shades split the values above the threshold into 2 or 3 bands. Contour lines trace where the value equals the threshold, between the cell centres.
Does a lone agent go straight?
Yes. On an empty grid all three sensors read the same, so it never turns: our tests run one agent for 50 steps and it moves exactly one step length each time in the same direction, wrapping round the edge.
Is the run the same every time?
Yes. The start and every random turn come from the seed, so the same settings give the same network, bit for bit; our tests check this and check the tool against a second agent step and spreading step of our own.
How big can it go?
Grids up to 400 × 400, up to 50,000 agents and 3,000 steps, with steps × (agents + 4 × cells) at most 360 million. The steps run in short chunks with a progress line so the page stays usable; every preset draws in under 2 seconds in our tests.
Can it print at real size?
Yes, when the drawing fits on one sheet: choose Real size and set the length of one unit (or one cell). Every printed point is within 0.2 mm of its true place in our tests, on US Letter and A4, as long as you print at 100% (Actual size); the check bar in the footer lets you confirm the scale. Bigger drawings print fitted to the page.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. Every agent move and every trail update is worked out by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.