*** Mandelbrot Art Challenge *** The Mandelbrot Set is a fractal you can zoom in on. Find a beautiful zoomed area, colour it, and share it. No programming required! Just run, then remix. *** Brief Instructions *** 0) If necessary, press <Space> to show the controls. 1) Click the picture to zoom in and find an interesting pattern. Zoom near the black outline for best results! 2) Choose a Colour Scheme. 3) Press <Space> to hide the controls. 4) Remix with your picture showing. Put your remix project in this studio: https://scratch.mit.edu/studios/8315880/ Mandelbrot Zoom - Full Instructions **************************************** * Zoom * When you click on the picture, the project will zoom in at the position of the mouse. You can Zoom many many times! You do not have to wait until a drawing is complete before zooming in again. Zoom first near the black outline for best results! Pictures with more black colour take longer to draw. The project draws a low resolution Preview picture, then a slower High Resolution picture . The "Show Zoom Area" button displays a rectangle showing the next zoom area. Adjust Next Zoom to 1, 2, 3 or 4 before zooming. Setting Next Zoom to 1 lets you shift the picture to a new centre. (The Zoom does not change). * <Space> key * The <Space> key hides or shows the controls. You cannot zoom while the controls are hidden. * Depth * There are three Depth settings: 50, 100 and 200. Increasing Depth increases the detail in the picture but is slower. I recommend you leave Depth at 50 while you create your design (faster) , then maybe increase Depth. * Colour Scheme * I recommend you Zoom to create your interesting design, then try many Colour Schemes. The project runs much faster if you only change the Colour Scheme! Note that colours change when you change Depth. * Save Your Design * Press <Space> to hide the controls. Remix the project. NB. If you want to make another design, it is easiest to run my original project again! If you "See inside" your own project, it usually autosaves with any changes you have made. So to make another design using your project, you should "See inside" before making any changes then use "File, Save as a Copy". * Save Your Design - 2 * You can press the Save button to get a Save Code. Other Scratchers can Load this code, but the design will be drawn slower than if you remixed the project as the data for each pixel is not saved. * <Undo> button * 10 levels of undo to go back to a previous zoom and centre. Note that there is no Undo for Colour Scheme or Depth as you can just select the previous Colour Scheme or Depth to go back. * Load Codes * Press the Load button to enter a code that has previously been saved using the Save button. You can also enter parameters from other internet Mandelbrot projects in the format: Real#Imaginary#Zoom#Depth#Colour Scheme# eg. -0.57#-0.65#32#50#12# Note that huge Depth values would make the calculations and drawing very slow. You need to add a colour scheme value (1 to 12). * A few example Load Codes * -0.57#-0.65#32#50#12# -0.160208#1.03292#96#50#4# -1.254#0.3842#128#50#7# -0.722396#0.357604#128#50#5# * The 12 Colour Schemes * 1 - Blue, Green and Red with overflows 2 - Green, Blue and Red with overflows 3 - Black and White (often very effective!) 4 - Colours used on this Wikipedia page: https://en.wikipedia.org/wiki/Mandelbrot_set 5 - Bands of Colour Gradients with many colours 6 - Bands of Colour Gradients Red-Red/Green-Blue-Blue/Red-Green-Green/Blue 7 - Bands of Colour Gradients Blue-Green-Red-Orange-Yellow-White 8 - Same Bands of Colour Gradients as 7 but colours are spread more evenly with Histogram Colouring. https://en.wikipedia.org/wiki/Mandelbrot_set 9 - Scratch Colors 1-100 all with Saturation 100 and Brightness 100. These are like rainbow colours. Scratch uses the hsb (hue, saturation, brightness) colour model. (Other Colour Schemes here are RGB) 10 - Green 11 - Grayscale 12 - Red Programmers who understand RGB or hsb colour can replace some of these Colour Schemes with their own.
Mandelbrot Art Challenge Studio: https://scratch.mit.edu/studios/8315880/ *** Many stunning remixes in the studio already! *** * Lag * This project executes over 85 million Scratch Blocks to draw one Mandelbrot design. (calculation is below) Scratch is not a fast computer language so it takes over 30 seconds on my PC to run these 85 million Scratch Blocks to draw one design. There are 172,800 (480 x 360) pixels on the stage. This project executes over 500 Scratch Blocks on average to calculate the colour of each pixel. So the project executes over 85 million (172,800 x 500) Scratch Blocks to draw one Mandelbrot design. This increases to over 340 million Scratch Blocks on average if Depth is increased from 50 to 200. Other programming languages may run 100 times or 1000 times faster than Scratch, so 30 seconds may become 0.03 seconds to draw a Mandelbrot Fractal. * forkphorus https://forkphorus.github.io/forkphorus/#305593150 runs this project faster (it is a site outside Scratch that compiles Scratch projects to speed them up). @CalculatorFun brought forkphosphorus to my attention in the project comments. * Other Mandelbrot Projects * Here is an example of a faster project (not part of the Scratch wesite) that I found on the Internet: http://www.jakebakermaths.org.uk/maths/mandelbrot/canvasmandelbrotv12bak7512.html I think this project by @twins_paradox is one of the best Mandelbrot projects on Scratch: https://scratch.mit.edu/projects/13858131/ * The Mandelbrot Set * The Mandelbrot Set (the black area of the picture) was defined and named by Adrien Douady in tribute to the mathematician Benoit Mandelbrot. (Wikipedia) https://en.wikipedia.org/wiki/Mandelbrot_set In Mathematics at school we are taught that there is no square root of -1. But mathematicians invented a set of numbers with rules that allow the square root of -1. These are called Complex Numbers and they have Real and Imaginary parts. This math is used to create the Mandelbrot Set but fortunately you don't need to know anything about the math to draw with this project. * Smooth Colouring * Smooth Colouring cf. distinct Colour Values is discussed on Wikipedia: https://en.wikipedia.org/wiki/Mandelbrot_set I used the similar formula below to smooth values but I am not sure which website I got it from: iterations = iterations + 1 - log(log2(abs(z)) * Wikipedia Colours * Wikipedia Colours List for Colour Scheme 4 from: https://stackoverflow.com/questions/16500656/which-color-gradient-is-used-to-color-mandelbrot-in-wikipedia
