Spirograph Maker vs Fractally

Create mesmerizing geometric art with a single tap. Released in 2017 with over 110,000 downloads — a math-meets-art tool refined over 9 years. Spirograph Maker turns the timeless mechanical drawing toy into a digital playground for your iPhone and iPad. Choose your gears, pick your colors, and watch hypnotic patterns bloom across the screen — no drawing skill required. WHERE MATH MEETS ART The patterns Spirograph creates aren't accidents — they're governed by GCD/LCM and parametric equations. Watch how the lobe count is determined by n/gcd(n,m), see hypotrochoids and epitrochoids come alive on your screen. A visual companion for middle-school number theory and high-school parametric curves. Whether you're a curious learner, a math enthusiast, or just love beautiful patterns, this is where math becomes mesmerizing. In 2022, this app was acknowledged in an academic paper on algebraic combinatorics — the smoothness criteria for Positroid varieties (Billey & Weaver, arXiv:2207.06508). From a child's toy to cutting-edge mathematical research — that's how deep these patterns go. FOUR GEAR SHAPES Not just circles. Draw with ellipse, rounded triangle (a curve of constant width), and teardrop gears too. Change the gear's shape and the symmetry of the pattern changes with it: circles stay regular, ellipses stretch, triangles beat in threes, teardrops curve organically. A strength slider tunes each shape continuously — from nearly circular to a flat ellipse, or a sharply pointed triangle or teardrop. KEY FEATURES - Auto-draw mode: tap once and beautiful patterns appear on their own - Custom color palette with gradient mode for endless combinations - Adjustable gear shapes and sizes: circle / ellipse / rounded triangle / teardrop, plus tooth count - Save your creations directly to your Photo Library - Share to Instagram, Facebook, or anywhere - Full iPad support — a bigger canvas for finer detail - Light and Dark mode WHY SPIROGRAPH MAKER - A meditative break from a busy day — without leaving your phone - A visual bridge between middle-school math and university geometry - Inspired by the classic Spirograph toy, reimagined for modern iOS - Perfect for parents, students, artists, and math enthusiasts - Works offline, anywhere PERFECT FOR - Winding down before bed - Sparking creativity with kids - A short math meditation anytime - Making one-of-a-kind wallpapers - Sharing unique art on Instagram - A short, calm focus break during your day In Japan, downloads notably spike around the start of new school terms and summer breaks — pointing to a growing use as a learning companion. Pull out your phone, tap once, and watch sacred geometry unfold. Whether you're a designer, a doodler, a student, or just love beautiful patterns, Spirograph Maker is the simplest way to make art that mesmerizes. Free to download. Optional ad-free upgrade available.

Fractally allows you to explore beautiful Mandelbrot and Julia set images, while at the same time, helping you gain a greater understanding of what they are. * interactively zoom and scroll around the images, using standard pinch and scroll gestures. * watch to see how the Julia set changes as you pan and scroll around the Mandelbrot. * view Mandelbrot or Julia point orbits, a visual representation of how a point changes as it moves through the iteration. * many different color schemes are provided. * control the amount of detail shown through the iteration editor. Over 2,000 iterations per point are possible. * zoom into the fractals over 1,000,000,000,000 x. * save and share your favorites, in the app as well as through Messages, Mail and AirDrop. * save high quality, large or small, anti-aliased images. Note that the saved images can range in size from thumbnails to wall sized photographs, depending on the amount of memory in your device. Images are saved in the lossless PNG image format. As you find interesting images, share them with your friends. Fractally saves fractal coordinates in a fractally file. When these files are shared with others, they can use the app to explore the region you found. To help understand the images being shown, try experimenting with low iteration counts, starting at 2, and moving up in steps of 1. As you slowly increase the iteration count, watch to see how the images evolve. At the other extreme, high maximum iterations can be used to reveal great hidden detail in deep zooms. Fractally is a fresh and clean implementation of the Mandelbrot and Julia sets. No frills, just a high quality, solid, viewer and image generator. Available, and free, on iPhone, iPad and the Mac. Donations are welcome and appreciated. For more details, please visit the support website. * privacy policy: https://luckgrib.com/fractally/privacy.html * terms of use: https://luckgrib.com/fractally/terms-of-use.html * end user license agreement: https://www.apple.com/legal/internet-services/itunes/dev/stdeula/