![]() Regardless, it's an interesting problem, and I'm thinking that the "best" solution should work for either finite or infinite iterations (though the latter is far more difficult due to the inability to calculate meaningful values for limits of various values that might be useful in the finite case). Since the edge is rough (i.e., there is no normal for any given point on the edge) a whole lot of things stop working. It becomes a much more interesting problem if you have to work at infinite iteration, since, even if you find a point that is on the edge (i.e., a points such that (x,y) is inside and (x+epsilon*cos(theta),y+epsilon*sin(theta)), I'm not convinced there is even a way to find the next point (assuming that theta is the direction your hand is in, and your "facing" theta + pi / 4). That's not exactly true - the Mandelbrot set has infinite circumference (and so does every branch of it), so while that strategy would work in theory, in practice, not so much. However, you can connect the two points with the 2 connected green lines. Most other paths would just take one line, but the top (or bottom) to the left is the most difficult 'route'). At iteration 10, the 'hardest' path that you can choose which maximizes the number of connected straight lines is 7, which is from the bottom to the top.Īt iteration 1 or iteration 2: Max = 1 line (since it's a circle, any part can be reached from a single line max to any other part)Īt iteration 3: Max = 2 lines (slightly warped circle, so to get from the top to the left, you need to connect two straight lines. Some paths only require two straight lines, some only one. ![]() The idea is to reach any part of the Mandelbrot from any other part. does not ship products or samples.I don't understand your example why would 7 be the maximum number of lines at iteration 10? In fact, don't you mean minimum number of lines? Wouldn't the maximum number always be infinity? This website is a news website that provides information about an offers across the internet to the best of our ability at the time of publication. Images are for representative purposes only. These parties not support, sponsor or endorse this website or its content, or services. The third-party product names, logos, brands, and trademarks are the property of their respective owners and not affiliated with. THIS CONTENT IS PROVIDED ‘AS IS’ AND IS SUBJECT TO CHANGE OR REMOVAL AT ANY TIME. ![]() Amazon, any store or brand displayed on this website does not support, sponsor or endorse this website or its content. CERTAIN CONTENT THAT APPEARS ON THIS SITE COMES FROM AMAZON SERVICES LLC. Content, discounts, offers, images, prices and availability are subject to change or removal at any time. is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to. Any price and availability information displayed on Amazon at the time of purchase will apply to the purchase of this product. Product prices and availability are accurate as of the date/time indicated and are subject to change. Important Disclaimer:We may get commissions for products or services purchased via links on our site. Looking for more mind benders? Try Logic Lovely for more mazes, sudoku, riddles and more. If you have any questions or need help just contact us here. I hope you liked these mazes, if you did please share them with a friend or family member whom may like it to help support more mazes in the future. And making your brain learn new things is what helps guard against memory loss. Solving maze puzzles gets those parts of the brain working again. But, once we figure things out, we do them without thinking. How can something like maze puzzles help your brain? If you think about it, we use our maze solving skills all through life – when we figure out how to get somewhere or the best way to do something. Or download insanely difficult mazes just to see what they’re like. Easier mazes are great for the kids – or to get you started on maze puzzles. At each difficulty level, there are downloadable PDFs with 20 mazes you can download and print out. We’ve got all mazes on this page divided by how complex they are. Because what’s better than doing something that’s not only fun, but challenges your brain – and for free! Just because we could, we created this boat load of maze puzzles that we’re offering to our readers.
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