Mandelbrot

Mesham is a type oriented programming language allowing the writing of high performance parallel codes which are efficient yet simple to write and maintain

Overview


The mandlebrot example will compute the Mandlebrot set over any number of processes. This is a set of points in the complex plane, the boundary of which forms a fractal. The mathematics, which are quite simple, behind the Mandlebrot computation really do not matter for our purposes. The important issue is that firstly the calculation is embrasingly parallel (i.e. simple and natural to parallelise) and secondly will produce an image which the user can identify with.

The algorithm itself is actually quite simple, with a relatively large proportion of it dealing with specific colourisation of the resulting fractal. The example on this page is purposly basic so that the potential programmer can understand it.



Performance


The Mandelbrot example was evaluated against one written in C-MPI on a super computing cluster. Below is the graph detailing the performance of such codes, due to the close performance of the codes when run on an initial number of processors was the same and as such not shown. Due to the embarrassingly parallel nature of this problem the advantages of using Mesham in terms of performance do not start to stand out until a large number of processors is reached.



Source Code
typevar pixel::=record["r",Int,"g",Int,"b",Int]; var pnum:=16; // number of processes to run this on var hxres:=512; var hyres:=512; var magnify:=1; var itermax:=1000; function Int iteratePixel(var hy:Float, var hx:Float) { var cx:Double; cx:=((((hx / hxres) - 0.5) / magnify) * 3) - 0.7; var cy:Double; cy:=(((hy / hyres) - 0.5) / magnify) * 3; var x:Double; var y:Double; var iteration; for iteration from 1 to itermax { var xx:=((x * x) - (y * y)) + cx; y:= ((2 * x) * y) + cy; x:=xx; if (((x * x) + (y * y)) > 100) { return iteration; };   };    return -1; }; function void main { var mydata:array[pixel,hxres,hyres] :: allocated[single[on[0]]]; var p;   par p from 0 to pnum - 1 { var tempd:array[record["r",Int,"g",Int,"b",Int], hyres]; var myStart:=p * (hyres / pnum); var hy:Int; for hy from myStart to (myStart + (hyres / pnum)) - 1 { var hx; for hx from 0 to hxres - 1 { var iteration := iteratePixel(hy, hx); tempd[hx]:=determinePixelColour(iteration); };         mydata[hy]:=tempd; sync mydata; };   };    proc 0 { createImageFile("picture.ppm", mydata); }; }; function pixel determinePixelColour(var iteration:Int) { var singlePixel:pixel; if (iteration > -1) { singlePixel.b:=(iteration * 10) + 100; singlePixel.r:=(iteration * 3) + 50; singlePixel.g:=(iteration * 3)+ 50; if (iteration > 25) { singlePixel.b:=0; singlePixel.r:=(iteration * 10); singlePixel.g:=(iteration * 5); };       if (singlePixel.b > 255) singlePixel.b:=255; if (singlePixel.r > 255) singlePixel.r:=255; if (singlePixel.g > 255) singlePixel.g:=255; } else { singlePixel.r:=0; singlePixel.g:=0; singlePixel.b:=0; };   return singlePixel; }; function void createImageFile(var name:String, var mydata:array[pixel,hxres,hyres]) { var file:=open(name,"w"); writestring(file,"P6\n# CREATOR: LOGS Program\n"); writestring(file,itostring(hyres)); writestring(file," "); writestring(file,itostring(hxres)); writestring(file,"\n255\n"); // now write data into the file var j;   for j from 0 to hyres - 1 { var i;      for i from 0 to hxres - 1 { writebinary(file,mydata[j][i].r); writebinary(file,mydata[j][i].g); writebinary(file,mydata[j][i].b); };   };    close(file); };
 * 1) include 
 * 2) include

This code is compatible with Mesham version 1.0 and later

Download
You can download the Mandelbrot example here or a legacy Mesham 0.5 version here