RealMandelRender vs FractalEcho

This "RealMandelRender" is an iOS app that utilizes WebGL 2.0's transform feedback to render Mandelbrot sets in real-time. It allows high-precision rendering up to quad float (128-bit) with a variety of color options. You can draw the Mandelbrot set using various parameters, but if you're not sure, simply press the "RANDOM" button to enjoy a variety of images! You can use drag and pinch gestures to move and zoom the image. Tapping the arrow in the lower right corner toggles the menu on/off. You can adjust various parameters to freely draw Mandelbrot sets. Instructions with images on how to use the app are available at the following URL: https://minnano.app/support/realmandelrender/how-to-operate/ ① ITERATION The Mandelbrot set is drawn by repeatedly calculating the following equation. In section ①, you control the number of iterations. Zn+1 = Zn * Zn + C CALCS/FRAME Specifies the number of calculations per frame. If the app feels heavy, try reducing this value to lessen the rendering load. However, setting this value too low can result in flickering of the shape during drag/pinch operations. CALCS/LIMIT Sets the upper limit for the number of calculations. Increasing this value allows detailed rendering of intricate parts of the shape. Conversely, lowering this value results in a rougher representation, but it might reveal interesting shapes during the rendering process. ② PRECISION Selects the rendering precision. Higher precision allows accurate rendering even when zoomed in but increases rendering load. You can choose from 32-bit, 64-bit, and 128-bit. Larger values result in higher rendering accuracy. Enabling the "AUTO" option automatically adjusts the rendering precision based on the zoom level of the shape. (To select 128-bit, you need to turn on the "SHOW PREC 128 BIT" option in the following ⑥ HIGH LOAD section.) ③ CENTER FIX Fixes the center coordinates of the image, preventing the shape from moving when dragged. SHOW Displays a crosshair to indicate the center coordinates of the image. ④ DATA COLOR Changes the color pattern used for rendering the shape. TOUR Allows selection and display of over 100 recommended scenic points for viewing. ⑤ OTHER INFO Displays coordinates, zoom level, and iteration count at the top of the screen. Tapping the displayed coordinates or zoom level opens a pop-up for editing. You can directly specify coordinates and zoom level by editing this text and selecting "UPDATE." Additionally, saving this text in a note-taking app allows you to easily access your favorite points. The meanings of each symbol are as follows: RE: Real Axis IM: Imaginary Axis SC: Scale IT: Iteration Count FPS Displays the frames per second (FPS) on the bottom left corner of the screen. Useful for monitoring rendering load. RANDOM Randomly selects and displays one of the recommended scenic points. If you're not sure how to adjust the parameters, simply press this button to enjoy various images. ⑥ HIGH LOAD In this section, settings for options that demand high rendering load are configured. The option values in this section are not saved and will be turned off every time the application is launched for safety reasons. If you have the latest iPhone/iPad, use the options in this section to fully enjoy beautiful images. HIGH DPI Displays images with higher dot density. LIMIT × 10 Sets the calculation limit to ten times the value displayed in "CALCS/LIMIT." NO LIMIT Calculates indefinitely without an upper limit for iterations. SHOW PREC 128 BIT Adds the option to select 128-bit precision alongside 32-bit and 64-bit in rendering accuracy. *Note: Enabling the "SHOW PREC 128 BIT" option alone does not enable rendering in 128-bit precision. After enabling it, you also need to select 128-bit precision in the ② PRECISION section.

Discover the mesmerizing world of fractals with FractalEcho, a powerful app that brings stunning visuals through virtually unlimited search capabilities to your fingertips. Explore intricate patterns that were once limited to supercomputers now accessible on your device. Unrivaled Search Depth and Resolution: FractalEcho enables you to explore fractals at up to 1,000,000,000 iterations and resolutions of up to 1e-1100. Imagine one billion iteration searches at resolutions of over one thousand digits of accuracy! This level of detail enables you to uncover previously hidden depths and push beyond the boundaries previously thought possible. FractalEcho: Where Mathematical Precision Meets Artistic Wonder Unlock the captivating world of fractals with FractalEcho – a powerful and intuitive app that brings the beauty of infinite complexity to your fingertips. Explore intricate patterns, hidden depths, and breathtaking visuals previously confined to high-end computing, now accessible on your device. Unrivaled Depth & Resolution: Experience virtually unlimited fractal generation like never before! FractalEcho enables fractal exploration at up to 1,000,000,000 iterations with a stunning 1e-1100 resolution – far exceeding the capabilities of other apps. Discover fractals never before seen to push beyond the boundaries of visual exploration. Utilizing advanced real-time algorithms, FractalEcho delivers unparalleled resolutions. Explore & Customize: Delve into Mandelbrot and Julia Sets, bringing them to life with animated colors, dynamic color palettes, and precise control over search depth, zoom levels, and color rates of change. Experiment endlessly to discover stunning new forms. A Unique Educational Tool: FractalEcho uniquely calculates both the border length and area of the fractal at any given iteration level, visually demonstrating the fascinating concept of an infinite boundary contained within a finite space – a core principle of fractals. Community & Sharing: Discover a vibrant gallery showcasing stunning fractals uncovered by other users. Save your favorite discoveries with bookmarks and personal notes. Share your own artistic discoveries with the world – export high-resolution graphics and fractal data for others to enjoy. Easy to Use: An in-app tutorial guides you through FractalEcho’s powerful features, making fractal exploration accessible to everyone. Whether you're a math enthusiast, an artist, or simply curious about the fractal universe, FractalEcho offers something for you. To illustrate the extreme resolution FractalEcho achieves, consider a comparison between two extremes: the most distant known galaxy (JADES-GS-z14-0) estimated to be 33.6 billion (33.6e+9) light years away, and an electron within an atom having an estimated diameter of about 5.636e-15 meters. The electron diameter is about 1.78e-41 times the distance to the farthest known galaxy. This is a number with 41 digits after the decimal point. FractalEcho’s resolution of 1e-1100 is over 1e1050 times more accurate than this comparison. To put it another way, if we measured the distance to the farthest known galaxy in units of electron diameters, FractalEcho's calculations would still be 1e1050 times more accurate. To represent FractalEcho’s accuracy in writing would require a decimal place followed by 1,100 zeros before the first non zero digit ie: 0.00000000…..1. Perfect for math enthusiasts and artists! Download FractalEcho and begin your journey into the infinite beauty of fractals! Visit https://FractalEcho.com to learn more. Some features require in-app purchases that can be shared across all your Macs, iPhones, and iPads. View our on-line gallery at: https://data.bluestonepond.com/FrE/FrE_Action/FrE_Gallery.php View our privacy policy at: https://fractalecho.com/FractalEchoPP/FrE_PrivacyPolicy.html View our terms of service policy at: https://fractalecho.com/FractalEchoPP/FrE_TermsOfUse.html