# Thread:

1. ## Finding the error in area of mandelbrot set.

I'm not really sure where to post this...

Basically, I've used Maple to plot the Mandelbrot set.
The way its done is I have a 10000x10000 array that is filled with values between 0 and 1 where each value represents the colour of a pixel on a grid. 0 stands for a black pixel and is part of the set, 1 is white and all other entries are a shade of grey depending on how many iterations they take to diverge.
To find the area I simply counted the number of 0's in the array (it was only different to the actual value by 0.002%). How would I go about finding the error in this? As in, I'm restricted by the number of iterations I can use,so some pixels that are black may NOT be black if I had a powerful enough computer so that I could increase the max number of iterations.

The value calculated by pixel counting (by using a massively more powerful computer than mine) is 1.50659177 $\pm$ 0.00000008.
The value I calculated was 1.506628382.

2. The inaccuracies obviously occur near the boundary of the set. Can you modify your program so that it recognises when a black pixel has a non-black neighbour? There will presumably be comparatively few of these, and you could then increase the number of iterations for those pixels.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9566947221755981, "perplexity_flag": "head"}