Vector Field vs Vectors and Planes

Vector Field lets you create and visualize mathematical vector fields with thousands of animated particles. Enter your own equations, adjust the simulation instantly, and watch how particles move through 2D, 3D, or spherical spaces. Whether you are studying differential equations, experimenting with dynamical systems, teaching vector calculus, or simply exploring mathematical patterns, Vector Field turns equations into interactive motion. Features: • Visualize vector fields in 2D, 3D, and on a sphere • Define custom dx, dy, and dz equations using x, y, z, and time t • Use built-in function presets or save your own • Adjust particle speed, density, lifetime, colors, and ranges • Animate time-dependent fields • Normalize vectors to focus on direction • Rotate 3D views interactively • Powered by Metal for smooth real-time rendering • Create, tweak, and discover vector fields directly from your device.

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.