surface example

3D Checkerboard Surface Graph

A stepped checkerboard made from quantized waves.

z = floor(abs(sin(x) * sin(y)) * 4) / 4

Quick facts

  • Formula: z = floor(abs(sin(x) * sin(y)) * 4) / 4
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The floor function turns smooth variation into flat levels.

Where it appears in calculus

It is useful for showing discontinuities and quantization.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. 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.

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Teacher prompt

Question: Why are there flat steps?

Answer: The floor function groups nearby heights into fixed levels.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Fourier Demo Surface

z = sin(x) + sin(2*y)/2 + sin(3*x)/3

A layered wave made from several sine terms.

Distance Field

z = min(sqrt((x - 2)^2 + y^2), sqrt((x + 2)^2 + y^2))

A surface showing distance to the nearer of two points.

Elliptic Gaussian

z = exp(-(x^2 / 8 + y^2 / 2))

A stretched bell surface with different widths by axis.

Anisotropic Paraboloid

z = x^2 / 4 + y^2

A bowl that curves more sharply along y than x.

Two Peak Surface

z = exp(-((x - 2)^2 + y^2)) + exp(-((x + 2)^2 + y^2))

Two smooth hills separated along the x-axis.

Basin and Ridge

z = x^2 - cos(3*y)

A parabolic basin crossed by repeated ridges.

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

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Worksheet Export

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How to Graph z=f(x,y)

Step-by-step guide for beginners