Make Chirps vs Drawing with Math

This educational app displays gravitational wave chirps created by mergers of massive black holes in several different ways, giving users an intuitive understanding of these exotic disturbances of space-time itself produced by cataclysmic events in distant galaxies. FEATURES: • Simulation: Experience the intricate behavior of gravitational waves through physics simulation of inspiralling black holes that merge to form a final black hole which then “shakes off” its excess energy. • Visualizations: See the essence of gravitational waves via waveform plots, frequency evolutions, and spectrograms, to understand the patterns and how they depend on black hole masses. • Auditory Experience: Listen closely as you hear the evolution of gravitational waves, detecting the characteristic increase in time in strength and frequency. Try varying masses to see how pitch is affected. • Dynamic Animations: Witness the captivating dance of black holes in collision animations. Explore the propagation of these waves through space-time with mesmerizing spiral animations. • Educational Insights: Gain a comprehensive understanding of gravitational waves and the pioneering work of LIGO through informative text pages, enhancing your knowledge of these cosmic phenomena. COMPATIBILITY Compatible with iPhone and iPad, iOS 16 or later. ACKNOWLEDGEMENT Supported by the National Science Foundation with grant PHY-2110181.

Our “Drawing with Math (Vector and Pixel Art)” app combines two main components: * uniquely versatile image editors, * various methods of linear transformations of both user-entered and system images. Image editors are available in vector and pixelated forms. The editors offer such options as: * free drawing, * entry of all standard shapes, * entry of regular Cartesian, polar, or parametric function into image editor. List of several visually appealing functions is provided. The App stores 10 most recent user entries for each type. Vector images can be linearly transformed in a variety of user-defined ways: * 2x2 matrix, * eigenvalues and eigenvectors, * rotation by degree, * reflection across a given vector. Pixelated images can be compressed by segments to user-selected rank. Mathematical context for the above is provided, whenever possible. Explanation of image compression algorithms requires significant understanding of Linear Algebra, and is available in our “Matrix Solver Step by Step” app. Several bonus images with animations and editable greeting cards are also available. Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.