Fractal Generator vs Polynomial Solver Step by Step

Fractal Generator Explore the beauty of mathematics through fractals. Fractal Generator lets you create Iterated Function System (IFS) fractals using both traditional mathematical methods and a new visual, drag-and-drop builder. Whether you’re learning linear transformations, teaching fractals in the classroom, or simply experimenting with mathematical art, the app makes fractals approachable and rewarding to explore. Create Fractals Analytically • Build fractals using classic affine transformation coefficients • Enter and edit values directly • Render self-similar fractals in real time Fractals are generated from systems of equations that describe how points are transformed. These systems can be solved using substitution, elimination, or matrices, making the app a natural companion for algebra and linear algebra coursework. New in Version 2.0 — Visual Fractal Builder Design fractals visually by placing and manipulating shapes on a grid. The visual builder converts geometric transformations into the underlying mathematical coefficients automatically, allowing you to: • Experiment without starting from equations • See how transformations affect the final fractal • Better understand how IFS systems are constructed This makes fractals more intuitive, especially for visual learners. Learn, Experiment, and Explore • Recreate classic fractals included in the app • Modify existing systems or create your own • Watch a built-in tutorial explaining how the math behind fractals works Export and Share • Export high-resolution images • Optional transparent backgrounds for PNG export • Save to Photos or share your creations easily Fractal Generator Pro Unlock the full experience with a one-time Pro upgrade: • All fractal collections • Visual drag-and-drop builder • Advanced export options No subscriptions. No accounts. No tracking. If you previously purchased any fractal pack, restoring purchases automatically unlocks Pro. Designed for iPhone, iPad, and Mac Support: support@lightbulblearninglogic.com Privacy Policy: https://lightbulblearninglogic.com/privacy-policy/

Polynomial Solver Step by Step is a calculator, and, more importantly, a teaching tool. It is designed to help students of both basic and advanced levels. Basic Algebra functions: 1. Polynomial multiplication. 2. Polynomial long division with step by step explanation. 3. Algorithm for finding rational roots consisting of the following: a. Finding all possible rational roots. b. Eliminating the roots outside bounds. c. Performing polynomial long division for each of the roots. d. Adjusting bounds based on long division results if appropriate. Iterative polynomial solving algorithms for advanced-level students: 1. Durand-Kerner method. 2. Aberth method. 3. Newton method with both real and complex starting points. 4. Global (also known as "damped") Newton method with both real and complex starting points. 5. Laguerre method with both real and complex starting points. 6. Bairstow method. 7. Muller method. 8. Eigenvalues of ‘companion matrix’ (demonstration of QR algorithm for eigenvalue calculation is available in our “Matrix Solver Step by Step" app). Interactive graphs are available for: 1. Polynomial functions and their derivatives. 2. Aberth and Durand-Kerner method points on complex plane. 3. Newton, global Newton, Laguerre, and Muller algorithm steps. 4. Newton and global Newton method fractals / convergence images on complex plane 5. Laguerre method convergence images on complex plane 6 Bairstow method convergence images depending on initial approximation values. 7 Muller method convergence images depending on initial approximation values. (Images 4-7 have adjustable settings for area, resolution and shading). Links to online references are included. Please write to us if you like to have new features / chapters added! Developers welcome any feedback, please write to us at graphmath@aol.com.