Sorry. I omitted my PAR file in my previous post where I tried out SciWise's second version of his formula for integrating the differential of the Mandelbrot equation: I discovered that Richard's Fractint for Windows beta 5 (not for general distribution) that I use changes upper case letters in function names to lower case when writing parameter values out, (with the <b> key) -- so I changed the name of SciWise's function (f1cmandel) to all lower case letters to avoid this problem. --------- Start of PAR: ---------- IntgrDerivOfMset2a { ; Hal Lane; SciWise; Default color map ; SciWise's 2nd ver of integrating ; the deriv of the Mand equation. ; Bailout = 4; fn1 = exp; c=(0.5,0.5) ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=171113.par formulaname=f1cmandel function=exp passes=1 center-mag=0.866196/2.44249e-015/0.9461387 params=0.5/0.5/4/0 float=y maxiter=1000 inside=0 periodicity=6 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555<3>HHHKKKOOO<3>ccchhhmmmssszzz00z<3>z0z\ <3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zVV<3>zz\ V<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>h\ zz<2>hlz00S<3>S0S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES\ <3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKKS<2>QKSSKSSK\ QSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS0\ 0G<3>G0G<3>G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8G\ G8EG8CG8AG88<2>GE8GG8EG8CG8AG88G8<2>8GE8GG8EG8CG8A\ GBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>B\ GFBGGBFGBDGBCG000<6>000 } frm:f1cmandel(XAXIS) {; sciwiseg, Edward Montague ; ; Integral via derivative of Mset. x = Pixel c=real(p1) + imag(p1) bailoutTest = p2 u = fn1(c) y = 1 : y= 2*x*y+1 z = u - y x = x*x + Pixel |z| < bailoutTest } --------- End of PAR file ------------- - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Edward Montague Sent: Monday, November 13, 2017 9:50 PM To: Harold Lane <hallane@earthlink.net> Cc: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Subject: Re: [Fractint] Integration under differentiation . As usual Hal.Lane has produced something remarkable . Thinking about what I'm attempting to do , align a particular iteration of the derivative of the mandelbrot set with a unique value of a function , using a constant for the function variable seems more appropriate. Eventually the constant might be replaced with a parameter. Also in the future , the comparison might involve a more complicated differential equation ; however first things first . At some stage I shall use maxima cas to examine the results . Here's the new formula : f1cMandel(XAXIS) {;sciwiseg , Edward Montague ; ; Integral via derivative of Mset . x = Pixel c=(0.5,0.5) u = fn1(c) y = 1 : y= 2*x*y+1 z = u - y x = x*x + Pixel |z| < 0.01 } On Mon, Nov 13, 2017 at 10:11 PM, Harold Lane <hallane@earthlink.net> wrote:
The group might be able to do something with this . I changed the bailout value to 4 and was able to see a few more iterations than when it was 0.1 . I'm in the process of trying different functions and color maps.
I set p1 and the function in the z screen. With p1=0 (making the bailout be 4), the function exp() get iterations up into the 30's.
- Hal Lane
######################## # hallane@earthlink.net ########################
-------- Start of PAR file: ---------------- IntgrDerivOfMset { ; hhlane Colors from Jim Muth reset=2004 type=formula formulafile=basicer.frm formulaname=f1Mandelbrot passes=1 center-mag=-0.465582/0.0/1.0/1/ float=y maxiter=1000 inside=0 logmap= periodicity=6 colors=00054L65K76K87K98K99MAAOABQ9CS9EU9GW9IY8K_8\ La8Mc8NeAPcBQaDS`ETZGVYHWWIYVKZTL`SNaQOcPQdNRfMSgK\ UiJVjHXlGYmE_oD`pBaqA`oC`nD_mE_lFZkGZjIYiJYhKXgLXf\ MXeNWcPWbQVaRV`SU_TUZVTYWTXXSWYSVZSVZSV_SV_KWVCZQ4\ `L6aO7aQ9bTAbVBcXDc_EdaGddHefIehKfkMfmOfnQfnSfoU_o\ UZoVYoVXoWWpWVmXUjXTgYSdYQaZOZZPW_MT_JR`GQ`DM_BJYA\ F_6AY6BX6CW6CV7DT7ES8ER9FQAGPBGNBHMCILDIKEJJFKHFKG\ GLFHMEIMDJNBJOAKO9LP8MQ3PR5NQ7MQ9LQBJQDIQFHQGGQIEQ\ KDQMCQOAQQ9QS8QT7QU9PVAPWBPXCPYDPZFP_GP`HPaIPbJPcL\ PdMPeNPfOPgPPfSJgRMhQPiPSjOVkNYlM`mMcnLfoKipJlqIor\ HrsGusGwrIurJsrLqrMprOnrPlrQkrSiqTgqVeqWdqXbqZ`q__\ qaYqbWpdUpeTpfRphPpiOpkMplKpmJolInkHmjGmjGliFkhEjh\ EjgDifChfCgeBgdAfdAdc9ba8a_8_Y7YW6ZV3ZV5ZV6_W8_Y9`\ _B`aC`cE_eF_gHZhIZiKYjLYjMYjMWkLWkKWkKVkJVlJUlIUlI\ UlHUmHUmGUmGVmFWmEYnE_oDapDdrCgsCitBkuBmvAowAqx8ty\ 7wz6zz5zz3zz2zz1zz0zzTzzU }
frm:f1Mandelbrot(XAXIS) {;sciwiseg , Edward Montague ; ; | x' - fn1(Pixel) | < 0.1 ; ; Integral via derivative of Mset . x = Pixel test = (4 + p1) u = fn1(x) y = 1 : y= 2*x*y+1 z = u - y x = x*x + Pixel |z| < test } -------- End of PAR file ------------------
-----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Edward Montague Sent: Monday, November 13, 2017 12:22 AM To: Fractint and General Fractals Discussion < fractint@mailman.xmission.com> Subject: Re: [Fractint] Integration under differentiation .
Okay , this is a very basic example , doesn't look particularly interesting . It's as if integrals smooth away the fractal structure .
The group might be able to do someting with this .
f1Mandelbrot(XAXIS) {;sciwiseg , Edward Montague ; ; | x' - fn1(Pixel) | < 0.1 ; ; Integral via derivative of Mset . x = Pixel u = fn1(x) y = 1 : y= 2*x*y+1 z = u - y x = x*x + Pixel |z| < 0.1 }
On Sun, Nov 12, 2017 at 9:34 PM, Tony Hanmer <a.hanmer@gmail.com> wrote:
Sounds intriguing! Could we have some examples, please?
Tony Hanmer
On 12 November 2017 at 07:29, Edward Montague <sciwiseg@gmail.com> wrote:
Lets examine a very basic differential equation :
y' - fn1(x) = 0
this is a test condition that we're interested in , we might even relax this to :
| y' - fn1(x) | < epi , where epi is a small tolerance .
We're quite familiar with this in fractint .
Now suppose that we're able to generate y' and y , as iterated functions . Then when the aforementioned condition is satisfied we have a value for the integral of fn1(x) at x = Pixel ; this being y .
As available , via an earlier post of mine , a general formula for finding the derivative of an iterated function .
Initially this might just be examined as a fractal .
At this stage I really don't know what this might produce ; maybe some interesting fractals . _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint
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