Beautiful, thanks for sharing it.<div><br></div><div>Tony Hanmer</div><div>Tbilisi, Georgia (the OTHER Georgia)<br><br><div class="gmail_quote">On 1 November 2011 01:51, Mike Frazier <span dir="ltr">&lt;<a href="mailto:fractonorg@gmail.com">fractonorg@gmail.com</a>&gt;</span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div>In the past I had wanted to have multiple mandelbrots in the same image but I didn&#39;t want to do image side trickery like the white square method or use an if statement that switched the image from one to the other. I stumbled across a way to do just that using a simple formula similar to the one used to calculate parallel resistance. Anyone that has taken electrical engineering is familiar with the formula for parallel resistance:</div>

<div><br></div><div>rp = 1 / ( 1 / r1 + 1 / r2 )</div><div><br></div><div>If you put a mandelbrot equation at r1 and r2 with a different center point you have it. You can use different orders for each mandelbrot and have as many as you like by adding more 1 / rn terms. When the mandelbrots get close they interact in wierd ways. I made a short &lt; 1 Mb QuickTime movie of two mandelbrots flying past each other. Almost like two galaxies colliding.</div>

<div><br></div><div><a href="http://dl.dropbox.com/u/33642054/image/two_mandelbrots.mov" target="_blank">http://dl.dropbox.com/u/33642054/image/two_mandelbrots.mov</a></div><div><br></div><div>The parameter file for the center image of the movie is below:</div>

<div><br></div><div>Two_Mand { ; Exported from Fracton.</div><div> reset=2004 type=formula formulafile=fracton.frm</div><div> formulaname=F_20111031_1502 passes=1 float=y</div><div> center-mag=0/0/0.1904761928571428/1/0/0</div>

<div> params=0/2.5/0/0/0/0/0/0/0/0 maxiter=500</div><div> inside=1 proximity=0</div><div> colors=000511921D32H43L54P74T85X96`A7dB7hD8lE9pFAt\</div><div> GAxHBvGAtGArFApE9nD9lD9jC8hB8fA8dA7b97`87Z76X76V66\</div><div> T55G00I21L42O63R84UA5XC6_E7bG8eI9hKAkMBnOCqQDtSEwU\</div>

<div> FzWGyVFwUFvTEtSEsRDqQDpPCnNCmMBkLBjKAhJAfI9eH9cG8b\</div><div> F7`E7_D6YC6XB5VA5U94S84R73P63N52M42K31J21H10G00WGG\</div><div> YHF_IEaJDcKBeLAgM9iN8kO7nP6pQ5rR4tS3vT2xU1zW0wU0sS\</div><div> 0pR0lP0iN0eM0bK0ZI0WH0SF0OE0LC0HA1E91A71751C92FB2I\</div>

<div> D2LF2OH2SJ3VK3YM3`O3cQ3fS3iU4mW4pY4sZ4v`4t_4qY4nX4\</div><div> lV4iU4gS4dR4aP4_O4XM4VL3SJ3PI3NG3KF3HD3G00H11J22K3\</div><div> 3M44N55P66Q77S88T99VAAWBBYCC_DD`EEbFFcGGeHHfIIhJJi\</div><div> KKkLLlMMnNNoOOqPPsQQtRRvSSwTTyUUzWWwUUuSSrQQoOOlMM\</div>

<div> iKKgIIdGGaFFZDDWBBU99R77O55L33I11L44O76QA9TDCWGEYJ\</div><div> H`MJcPMeSOhURkXUn_WpbZse`vhcxkfwhcue`sbZq_WoXTmURk\</div><div> ROjOLhLJfIGdFDbCA`98Z65Y32W00G00I33K66M99ODDQGGTJJ\</div><div> VMMXPPZTT`WWbZZdaafddihhkkkigghddg``fYYeUUdRRcOOaK\</div>

<div> K`HH_DDZAAY66X33W00000000 }</div><div><br></div><div>frm:F_20111031_1502 {</div><div>; Two mandelbrots</div><div>; p1 is the position of mandelbrot 1</div><div>; p2 is the position of mandelbrot 2</div><div>; time = instant</div>

<div>z=0,</div><div>r1=p1,</div><div>r2=p2:</div><div>z1=1/(z*z+pixel-r1),</div><div>z2=1/(z*z+pixel-r2),</div><div>z=1/(z1+z2),</div><div>|z|&lt;=100</div><div>}</div><div><br></div><font color="#888888"><div><br></div>
-- <br>Mike Frazier<br>
<a href="http://www.fracton.org" target="_blank">www.fracton.org</a><br>
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<br></blockquote></div><br></div>