3D Damped Ripple Surface Graph
A ripple surface whose waves fade away from the origin.
z = sin(x^2 + y^2) / (1 + x^2 + y^2)Quick facts
- Formula: z = sin(x^2 + y^2) / (1 + x^2 + y^2)
- Category: surface
- Tags: surface, calculus, z=f(x,y)
What this graph represents
The denominator grows with distance and reduces the height of far-away oscillations.
Where it appears in calculus
Use it to show bounded oscillation and damping.
How to use this graph
- Rotate the surface by dragging with your mouse or finger
- Use the Embed button to copy an
<iframe>for your LMS or lesson page - Click PNG to export a classroom-ready image
- Click Formula or LaTeX to copy the equation for your notes
Embed this graph
Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.
Open embed pageTeacher prompt
Question: Why do the ripples get smaller?
Answer: The denominator grows as x and y move away from 0, shrinking the output.
Related graphs
Explore more surface examples and compare shapes, slices, and contour behavior.
Cone Surface
z = sqrt(x^2 + y^2)A circular cone rising from the origin.
Plane
z = 2*x - y + 1A flat plane with constant slope.
Tilted Wave Plane
z = 0.35*x + sin(y)A sloped plane with a wave running across it.
Sine Cosine Product
z = sin(x) * cos(y)A checkerboard-like wave surface.
Absolute Value Pyramid
z = abs(x) + abs(y)A four-sided pyramid made from absolute values.
Cubic Surface
z = x^3 - yA cubic sheet tilted by the y term.
Explore more tools
Use these free browser tools to extend your graphing workflow.