Mandelbrot Set Explorer 3.3D
Game Introduction
NOTES: Every pixel on the rendered drawing is the result of a repeated calculation -- the number of times it is repeated (its Dwell value) determines the color of the pixel. Information about the Mandelbrot Set can be found on the Web. Good examples: http://en.wikipedia.org/wiki/Mandelbrot_set http://www.math.utah.edu/~pa/math/mandelbrot/ Rendering takes place in successively smaller and smaller rectangles. This is done because, if every pixel of an entire rectangle border has the same Dwell value, then every pixel in the entire rectangle inside can be set to that Dwell value -- WITHOUT HAVING TO CALCULATE EACH ONE. (This is called the Mariani/Silver Algorithm) This is a major time saver -- especially when there are large areas of the Black Mandelbrot Set in the scene. When this scene is rendering, and finds a rectangle that has all the same Dwell border, it displays a colored circle in the rectangle. Convolution Filter image processing information can be found here: https://en.wikipedia.org/wiki/Kernel_(image_processing) http://setosa.io/ev/image-kernels/ http://lodev.org/cgtutor/filtering.html 2019-02-24.... Timing test: r: -0.7570942786952887 i: 0.07340726794189592 Zoom: 41666666666666.666 Max Dwell: 20000 PC Windows 10 Firefox: 2567.1 seconds Phosphorus: 42.8 seconds iMac Firefox: 2600 seconds Phosphorus: 39.5 seconds Safari: 1533.6 seconds Phosphorus: 6.0 seconds !!!!! CREDITS: Thanks to Kouzeru and Project: https://scratch.mit.edu/projects/178564137/ for inspiring me to pursue my idea of adding convolution filter image processing. Thanks to jpginn and Project: http://scratch.mit.edu/projects/10753622/ for the idea of rendering by rectangles (Silver Algorithm). Here's a web page that describes this Mariani/Silver Algorithm: http://www.mrob.com/pub/muency/marianisilveralgorithm.html
How To Play
-------> Use Turbo Mode!!!! <------- (Hold down Shift key while clicking Green Flag) ★★★★★ Version 3.3D ★★★★★ Draws the Mandelbrot Set. You can Zoom in and out and change the color pallet. You can now apply image processing (Emboss, Sharpen, Blur, Grey-Scale, Inverse) to improve the image. Emboss filter makes it look 3D! ★★★ Changes in 3.3D version from 2.5 version ★★★ ★ Rendering time has been improved! Rendering is up to 50% faster than the 2.0 & 2.5 versions, and up to 350% faster than the original version! (2.0 version: https://scratch.mit.edu/projects/13858131/ 2.5 version: https://scratch.mit.edu/projects/20912974/ Original: https://scratch.mit.edu/projects/10094995/ ) ★ Another color gradient pallet added: "Grad 5", as well as a second X-ray pallet: "X-ray2". ★ Set Zoom now goes up and down to 100x. ★ When entering coordinates (after pressing the E key), you now also enter the Max Dwell value. ★ Convolution Filters can be applied to the rendered image: Grey-Scale, Emboss, Sharpen, Blur and Inverse Color. - - - - - - - - - - - - - - - - - - - - - - - - - INSTRUCTIONS: Change the [Set Zoom], [Max Dwell] and [Draw Mode] settings, move (drag or arrow keys) the Magnifying Glass to where you would like to Zoom, and then click the triangular Draw button to render/draw the Mandelbrot Set. Click the square "Stop" button at any time during drawing to stop drawing. (You do not have to wait for the drawing to complete before zooming in again) The Magnifying Glass can be dragged to different locations. Also, the Right, Left, Up & Down arrow keys can be used to move the magnifying Glass one pixel in those directions. You can also press the E key to enter the r & i coordinates, zoom and Dwell values from the keyboard. Then press the triangular Draw button. After the scene is rendered, you can redraw it in another drawing mode without having to re-render it by ONLY changing the [Draw Mode] and clicking the green arrow. This takes just a few seconds to redraw the scene with the new color pallet. After the scene is rendered, you can apply convolution filters by pressing keys 1 thru 9: 1 - Make Grey-Scale 2 - 3x3 Emboss 3 - 5x5 Emboss 4 - 3x3 Emboss2 5 - 3x3 Sharpen 6 - 5x5 Sharpen 7 - 3x3 Sharpen2 8 - 3x3 Blur 9 - Inverse Colors The H key can be pressed to toggle on or off the Filter Button Help list. The F key can be pressed to toggle on or off the applied filters variable. This shows what filters have been applied to the scene. Go back to the original rendered scene by clicking the triangular Draw button. Special Keys: ★ 1-9: Applies Filtering to the rendered image. ★ C: Toggles (Hides/Shows) the Magnifying Glass Coordinates & Zoom value. ★ E: Enters the Enter mode so you can enter coordinates, Zoom and Dwell from the keyboard. ★ F: Toggles (Hides/Shows) the Filters variable. This shows what filters have been applied. ★ H: Toggles (Hides/Shows) the Filter Button HELP List. ★ M: Hides/Shows the magnifying Glass. ★ P: Toggles (Hides/Shows) the Pixel Status List. This shows pixel information about the rendered image. ★ S: Stops the fractal rendering, if it is currently rendering. ★ Arrow keys: Up, Down, Right, Left. These move the magnifying glass around the scene. - - - - - - - - - - - - - - - - - - - - - - - - - TIPS: ★ Zoom in on areas just outside (but not in) the Black areas. ★ Set [Max Dwell] to higher values when zooming in deeper and deeper. A Higher Dwell increases the resolution of areas near the Black area borders. But, this also takes more time to render. ★ Pressing the M key toggles (Hides/Shows) the Magnifying Glass. ★ Pressing the S key stops the drawing -- this is the same clicking the square "Stop" button. This does NOT stop any Convolution filtering that’s occurring. ★ Pressing the C key toggles (Hides/Shows) the Coordinates (r, i) and the Zoom amount. ★ Press the E key to enter coordinates and zoom. Good example: r: -0.153481792 i: 1.030177024 Zoom: 41667 Dwell: 600 This took 57 seconds on my laptop. ★Pressing the P key toggles (Hides/Shows) the Pixel Status List. This shows pixel information about the rendered image: "In Mandelbrot" are those pixels whose Dwell value reached the Max Dwell value. They are the pixels in the Black Area. "Outside Set" are those pixels that aren't "In Mandelbrot". These pixels are used for the Dwell Min & Max, and the Dwell Mean, Median and Mode calculations. "Skipped Pixels" are those that did not need to be calculated because they were within a rectangle that had its entire boundary pixels all the same value. ★ Emboss Filter works best on Grey-Scale scenes. Try it in Forkphorus!... https://forkphorus.github.io/app.html?id=181341231&turbo&w=480 The above example took under 2.2 seconds in Forkphorus.
Author
twins_paradox
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