------- Use Turbo Mode! ------- (Hold down Shift key while clicking Green Flag) Version 3.3D now available! https://scratch.mit.edu/projects/181341231/ ****** Version 2.5 ****** Draws the Mandelbrot Set. You can Zoom in and out. *** Changes in 2.5 version from 2.0 version *** * I was able to speed up rendering a bit. Render times are now approx. 90% of what they are for version 2.0. * I moved the key detect code to a separate sprite. I think this helps with some browsers and an issue with the [+] and [-] buttons. * After the scene renders, pressing the P key calculates and displays Pixel Statistics, and a List of the number of pixels for each Dwell value from 1 to Max Dwell (the Dwell Freq.). Pressing P again will hide these Pixel Statistics. * The Z key feature for the Magnifying Glass has been removed. * Scripts have been moved around and changed slightly. - - - - - - - - - - - - - - - - - - - - - - - - - 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 Start button to 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 around. Also, the Right, Left, Up & Down arrow keys can be used to move the magnifying Glass one pixel in those directions. 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. 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. * 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. * Pressing the C key toggles (Hides/Shows) the Coordinates (r, i) and the Zoom amount. --- NEW FEATURES! --- * Press the E key to enter coordinates and zoom. Good example: r: -0.153481792 i: 1.030177024 zoom: 41667 (use Max Dwell of 600 and Draw Mode: Grad 3) This took 91 seconds on my laptop. * Faster! 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 a major time saver -- especially when there are large areas of the Black Mandelbrot Set in the scene. When this project is rendering, and finds a rectangle that has all the same Dwell border, it displays a colored circle in the rectangle. Another time improvement over version 1.0 is better coding of the Dwell-calculation-iteration Block. * The Coordinates that show (after pressing the 'C' key) now show the coordinates when the Magnifying Glass is moved around. * More vivid colors than in version 1.0 * You can re-draw the rendered scene using a different Draw Mode by ONLY changing the Draw Mode and then pressing the Green Arrow. This takes just a few seconds. The scene doesn't need to be re-rendered. When a scene is rendered, the calculated Dwells for each pixel are now stored in memory. This makes it possible to re-draw the scene with a different Draw mode without having to recalculate each pixel's Dwell value (as in version 1.0) Having the pixel's Dwell values stored in memory makes it possible to draw the scene using a pen_size of 2, but a resolution of 1. This is done by starting the drawing at the top right and drawing down, one pixel at a time, and then starting the next column one pixel over to the right. This results in a much better looking drawing than how it was done in version 1.0 using a pen_size of 1. * Seven great Draw Modes (color gradients): Grad 1 Grad 2 Grad 3 Grad 4 (best used on deep dives) Metal Stripes X-ray * Added '50x' and 'out 50x' to the Set Zoom choices. * Holding down the Max Dwell '+' or '-' buttons for more than 3 seconds makes the Dwell change at a faster rate. This lets you to go to higher values faster. * Fixed what is shown in the Zoomed box. The zoomed value is no longer truncated. When it gets very big, it shows billions and trillions -- 'b' and 't' following the value.
** In the Pixel Stats List ** * "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. The buttons and text readouts are all done with sprites. 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/ I save each pixel's Dwell value into memory. I found that one huge array became extremely slow to use. Instead, I use 8 smaller arrays. Thanks to several Scratchers for the RGB (millions of colors) information. Thanks to jpginn and Project: http://scratch.mit.edu/projects/10753622/ for the idea of rendering by rectangles. Here's a web page that describes this Mariani/Silver Algorithm: http://www.mrob.com/pub/muency/marianisilveralgorithm.html Thanks to the Scratchers of other Mandelbrot projects for inspiration.
