. I recall the parallel resistance formula from my 4th grade advanced electronics class; something like if you have a number of resistors in parallel the total resistance is less than the least, like taking the inverse of all the inverses: Rt = 1 / (1/R1 + 1/R2 ...... + 1/Rx) or something like that. But what does it have to do with the fractal formula? I don't see it, except the last line has a similar format. Anyway, cool image. And if you zoom back a little you see the parent fractal - one of the freakyest Mandelbrot monsters I have ever seen! I will see if I can do a zoom animation of this. Gold is so like, way cool! .
Yes you have the parallel resistor formula correct. I was experimenting with different ways to combine two or more mandelbrot like equations and I thought I would try to combine them by putting a mandelbrot type equation at R1, R2, Rx in the parallel resistor formula. That works much better than just adding the terms together because the terms that are nearest zero dominate the equation (because of the 1/R). With this effect almost any combination of terms makes a fractal. The equation for the recent post is below. You can see a z^2 mandelbrot in f1,f2, and f3. Note that the three mandelbrots are centered at different locations because they have a different offset constant (the p1 parameter sets this). The mandelbrots also overlap and that is the key to getting different looking stuff. z=0,c1=pixel-p1,c2=pixel+p1,c3=pixel: f1=z*z+c1, f2=z*z+c2, f3=z*z+c3, z=1/(1/f1+1/f2+1/f3), I have posted several previous fractals using variations of the formula with different functions as almost anything works. I particularly like using sinh and cosh. Look in the gallery on my website at the last 3 links at the bottom of the page to see some other parallel resistor formula fractals. I made one movie that animated the location of the terms. The varying overlap created an interesting effect and you could kind of see what the equation did to overlapping features. The link to the gallery is: http://www.fracton.org/posts.html The movie one is at: http://www.fracton.org/fmlposts/mixing_cosine.html and is called Mixing Cosines. If you want to experiment with the formula try zooming out enough so you can see the parent fractal. Then set the overlap until something interesting happens. There are lots of interesting things in islands that appear in the center of things. I usually looked along the x axis since that has nice symmetry and speeds up the search. If you have time try some trig functions and higher powers of z as you can make some really nice higher order fractals. These are much more interesting than the usual high order fractals that tend to look all look the same. I enjoyed your last FOTD animation. I actually watched it several times. Feel free to do any animations with any of my posts. I look forward to seeing your creations. -- Mike Frazier www.fracton.org
When I double checked the links I realized I gave you the wrong one to the page with the movie. The correct link is: http://www.fracton.org/fmlposts/mixed_up_minibrot.htmland is called Mixed Up Minibrot. -- Mike Frazier www.fracton.org
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JackOfTradeZ＠comcast.net -
Mike Frazier