B.D., You said:
What really interests me with this formula is that when you find some parameters for p3 and start incrementing real(p5) from 1 to all the way up.
If you are not already using it, I recommend trying Fractint's Parameter Explorer/Evolver to investigate the effects of parameter changes. It's a useful tool for exploring the effects of a range of parameter values. It automatically creates a screenful of thumbnail images (which you control the number of and size of) made with a sequence of increments in value of your two chosen parameters -- shown located in X & Y on the grid of thumbnails. When I use the Evolver, I find I have to be quite careful when I specify the minimum and maximum values of the area of the fractal to calculate and show -- as well as the minimum and maximum values of the parameters to get what I want. The documentation for Fractint and its "Parameter Explorer/Evolver" is now online on Paul N. Lee's mirror of THE SPANKY FRACTAL DATABASE site -- conveniently broken out by sections here: http://www.nahee.com/spanky/www/fractint/findex.html The Evolver is in Section 5: Doodads, Bells, and Whistles Here's an example of its use -- showing the effect of varying the initial z value of the Mandelbrot set away from the critical point of (0,0): / CRITDEMO.jpg - Fractint's Parameter | Explorer / Evolver showing 81 M-sets perturbed | away from the critical value (0,0). | The real-perturbing value varies left to right; the | imaginary-perturbing value varies up and down. \ Anti-aliased: http://www.emarketingiseasy.com/TESTS/FOTD/2014/CRITDEMO.jpg It looks like I goofed and got the canonical critical point (0,0) one thumbnail image to the left of center... - Hal Lane ######################## # hallane@earthlink.net ######################## === Forwarded: ============================================= Author: B.D. V.C. Date: 2014-11-14 05:01 -500 To: Fractint and General Fractals Discussion Subject: Re: [Fractint] Anyone seen anything like this? Hello, Thank you for your answer. What the shape of ORDs02 is really similar to is a Julia set of -0.75+0i, it can be seen if real(p5) is raised, for example, to 20 or more. The first parameter below corresponds to the shape you have shown and I have included two more similar parameters, to show (in some sense) how these are possible. If z = c = pixel: ORDs04 is z = z*z +(c^2 +c) *3.5 ORDs05 is z = z*z +(c^2 +c) *-1 ORDs06 is z = z*z +(c^2 +c) *3 What really interests me with this formula is that when you find some parameters for p3 and start incrementing real(p5) from 1 to all the way up. Have a nice day B.D. ---parameters-start---------------------------------------- ORDs04 { reset=2099 type=formula formulaname=ORDs center-mag=-0.5/0/1.4/0.75/0 params=0/0/0/0/1/0/3.5/0/1/0 float=y maxiter=200 inside=0 periodicity=0 } ORDs05 { ; p3 = -1+0i Mandellambda reset=2099 type=formula formulaname=ORDs center-mag=-0.5/0/0.75/0.75/0 params=0/0/0/0/1/0/-1/0/1/0 float=y maxiter=200 inside=0 periodicity=0 } ORDs06 { ; p3 = 3+0i reset=2099 type=formula formulaname=ORDs center-mag=-0.5/0/1.3/0.75/0 params=0/0/0/0/1/0/3/0/1/0 float=y maxiter=200 inside=0 periodicity=0 } frm:ORDs { c = z0 = pixel, z = 0, c_param = p3, z_param = p4 level_n = 0, level = real(p5) ; integer > 0 bailout = 100 : IF (level_n >= 0) z0 = z0*z0 +c *c_param level_n = level_n +1 c = z0 IF (level_n == level) level_n = -1 z0 = c *z_param ENDIF ELSE z = z*z +z0 ENDIF |z| <= bailout } ---parameters-end------------------------------------------ === Forwarded: ============================================= -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com]On Behalf Of B.D. V.C. Sent: Thursday, November 13, 2014 2:40 PM To: fractint@mailman.xmission.com Subject: [Fractint] Anyone seen anything like this? Hello. Anyone seen anything like this? I couldn't find similar stuff, although I would like to. I included a formula (ORDs) with three sample and simpler parameter files and each parameter file has a corresponding small formula, to offer a not even slightly complete explanation about what is happening here. The formula ORDs01 corresponds to parameter file ORDs01 with real(p5) set to 3, formula ORDs02 corresponds to parameter file ORDs02 with real(p5) set to 3 also, while the formula ORDs03 creates the same image as parameter ORDs03. Thank you. ---parameters-start---------------------------------------- ORDs01 { reset=2099 type=formula formulaname=ORDs center-mag=-0.5/0/0.6666667/0.75 params=0/0/0/0/1/0/1/0/7/0 float=y maxiter=200 inside=0 periodicity=0 } ORDs02 { reset=2099 type=formula formulaname=ORDs center-mag=0.5/0/0.6666667/0.75 params=0/0/0/0/-1/0/1/0/10/0 float=y maxiter=200 inside=0 periodicity=0 } ORDs03 { reset=2099 type=formula formulaname=ORDs center-mag=-0.5/0/0.6666667/0.75 params=0/0/0/0/1/0/-1.5/0/1/0 float=y maxiter=200 inside=0 periodicity=0 } frm:ORDs { ; p3 = 1.0 +0.0i ; p4 = 1.0 +0.0i ; real(p5) = 8 c = z0 = pixel, z = 0, c_param = p3, z_param = p4 level_n = 0, level = real(p5) ; integer > 0 bailout = 100 : IF (level_n >= 0) z0 = z0*z0 +c *c_param level_n = level_n +1 c = z0 IF (level_n == level) level_n = -1 z0 = c *z_param ENDIF ELSE z = z*z +z0 ENDIF |z| <= bailout } ---parameters-end------------------------------------------ ---formulae-start------------------------------------------ ORDs01 { c = pixel, z = 0, bailout = 100 c = c^8 +c^7 *4 +c^6 *8 +c^5 *10 +c^4 *9 +c^3 *6 +c^2 *3 +c : z = z*z +c |z| <= bailout } ORDs02 { c = pixel, z = 0, bailout = 100 c = c^8 -c^7 *4 +c^6 *4 +c^5 *2 -c^4 *5 +c^3 *2 +c^2 -c : z = z*z +c |z| <= bailout } ORDs03 { c = pixel, z = 0, bailout = 100 c = (c^2 +c) *-1.5 : z = z*z +c |z| <= bailout } ---formulae-end-------------------------------------------- =========================================================== --- This email is free from viruses and malware because avast! 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