Open World Discover
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Pick a surface — the ground behind this page rebuilds itself while you watch. Then go down and walk it.
This is the ground at true proportions — 1 km of x is as long as 1 km of z. Drag the graph up or down to stretch or squash the z axis, the way you would shift-drag an axis in GeoGebra. The world rebuilds when you let go.
Every ridge, river and forest is generated from equations you can read. Fly it, drive it, walk it.
A two-kilometre island raised from fractal noise, carved by a hydraulic-erosion pass, then handed over with the mathematics left visible. Build your own terrain above and the ground rebuilds itself from any z = f(x, y) you can type; Esc in the field brings you back here to change it.
Your location is a vector. The HUD keeps P = [x, y, z] running as you move — coordinates stop being abstract the moment they are yours.
The directional derivative Duf rides along with every step, so a hill is never just a hill — it is a gradient you can feel.
Swap the island for sin(x)cos(y) and watch a textbook surface become weather-worn ground you can land a helicopter on.
Everything the world does with your equation, written down. No hidden rescaling of x or y — the only thing the engine decides for you is how tall to draw z.
The map is x, y ∈ [−1000, 1000]. One unit of x or y is exactly one metre of ground, so walking 100 m east is Δx = 100. x runs east, y runs north, z is up — the textbook right-handed set, and the HUD prints P = [x, y, z] in it.
The square is always dry: the lowest point of the graph is parked 10 m above sea level, so nothing inside can flood — no crater lakes in a paraboloid. Beyond the four sides a short rim drops to the sea floor. You cannot walk, drive or fly past the sides.
If the graph's natural relief already reads as terrain (60 – 400 m), z is drawn 1 : 1. Otherwise the whole z axis is multiplied by one round factor — 1, 2 or 5 × 10k — so the relief comes out near 220 m: x² + y² gets z : 1 = 0.0001 m, a shallow plane gets 1 = 1 m. The factor is printed under the equation and the HUD reports z in the function's own units, not in metres.
Where f has no real value — √ of a negative, division by zero, log of zero — the ground is the flat plane z = 0. Cobb–Douglas therefore rises only in the first quadrant and the other three are level fields at z = 0.
P = [x, y, z] is your place on the graph. Duf is the directional derivative along the way you are facing — the slope you are about to feel — computed from the same function that built the ground. The compass reads θ in radians, 0 at east, counter-clockwise, exactly as on paper.
+ − × ÷ ^ with ^ right-associative, unary minus, parentheses and implicit
products (2x, sin(x)cos(y)). Functions:
sin cos tan exp ln log sqrt abs min max; constants pi e.
A fresh visit always opens on the island; add ?f=x^2-y^2 to the address to
open straight onto that graph. The ground is shaped here only — press Esc in the
field to come back and change it.
W A S D move · Shift sprint · Space jump · Mouse look · T call the recon truck · H call the helicopter · E enter / exit · M full map · G holo compass · 1 2 3 / V render layers · Esc back to this page
It has been rendering live behind this page since you arrived. Go down and touch the ground.
Click to enter the field