• September 18, 2021, 11:58:40 PM

### Author Topic:  Natural Field Lines....  (Read 810 times)

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#### Chris_M_Thomasson

• Fractal Feline
• Posts: 175
• Programmer by trade; love fractals and math! :^)
##### Natural Field Lines....
« on: June 25, 2021, 10:39:23 PM »
My code is in the page, however, let me try to explain...

To draw a field line segment, we pick a point A on the plane... Then perform N iterations on the point using your fractal of choice. The Mandelbrot and Julia sets are shown here. So, after we finish with the N iterations we have a new point, call it B. We take the difference and angle between A and B. We can travel from A to B a short distance E, call E epsilon. We end up at a new point called C. We draw a line from A to C; set A to C, and repeat. This can generate a fairly interesting field, well at least to me.  We can even plot arrows on the lines. I have not implemented that yet. Anyway, here is a link to my online code where you can watch the field being drawn in real time. Also, you can click around on the canvas to generate field lines. Can your browser of choice get my work to, work?

http://fractallife247.com/test/

Click on the "Animation Testing 123" button to watch it draw the field.

This is all highly experimental, and I am just having some fun.

It's a Fractal Life, 247... ;^)

• Fractal Frankfurter
• Posts: 553
##### Re: Natural Field Lines....
« Reply #1 on: June 26, 2021, 06:46:10 AM »

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 175
• Programmer by trade; love fractals and math! :^)
##### Re: Natural Field Lines....
« Reply #2 on: June 26, 2021, 07:12:12 AM »
java script source

Its still in pre-alpha stage. But, it does seem to work on a vast variety of browsers and devices.

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 175
• Programmer by trade; love fractals and math! :^)
##### Re: Natural Field Lines....
« Reply #3 on: July 27, 2021, 09:52:35 PM »

#### cptryums

• Fractal Freshman
• Posts: 3
##### Re: Natural Field Lines....
« Reply #4 on: August 16, 2021, 08:20:35 AM »
Your technique is fascinating to me

At first I thought it was an bug in my implementation, but when i look closer again,I found that's a correct solution

It's kinda reminds me of

i implement them using your Implementation  select A (I get that value from grid sampling) and get B from IterateFunction then normalize vector from B to A and Multiply with Epsilon you will get point C , do this again until maxLineCount (i set it to 1000) is Reached

Draw line between A to C, then set A to C
i use bresenham line drawing algorithm

I use histogram approach in plot function

My coloring procedure as follows :
factor = log(CountOfHowManyDrawLine / SomeConstant + 1)
use this factor in any color palette that you like

I code all of them in JavaScript in html

i am not good at english btw ,I'm sorry for that

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 175
• Programmer by trade; love fractals and math! :^)
##### Re: Natural Field Lines....
« Reply #5 on: August 16, 2021, 10:21:46 PM »
EXCELLENT WORK!

What was the grid sampling resolutions? Your rendition looks very dense! Was it per-pixel?

Well done! Thank you very much!

#### cptryums

• Fractal Freshman
• Posts: 3
##### Re: Natural Field Lines....
« Reply #6 on: August 18, 2021, 11:28:42 AM »
my sampling resolution is at least 128 in all dimensions
sampling in visible region
my image size is about at least 1920x1440
(i forget exact value though)

was it per pixel ? no (for sure)

Instead I will re-render them to tell you

image size is 1920x1440

sampling size is 682x512

mandelbrot_iteration = 1000

line_iteration  = 100

line_epsilon = 1e-2

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 175
• Programmer by trade; love fractals and math! :^)
##### Re: Natural Field Lines....
« Reply #7 on: August 19, 2021, 03:18:37 AM »
EXCELLENT WORK!

What was the grid sampling resolutions? Your rendition looks very dense! Was it per-pixel?

Well done! Thank you very much!

The answers to my questions are there. Thanks again.

#### 3DickUlus

• Posts: 2460
##### Re: Natural Field Lines....
« Reply #8 on: August 19, 2021, 04:41:09 AM »
@cptryums that is one of the most fascinating "interpretations" of the mandelbrot set that I've ever seen.

Thank you @CMT for sharing your code, very well done

#### cptryums

• Fractal Freshman
• Posts: 3
##### Re: Natural Field Lines....
« Reply #9 on: August 21, 2021, 06:59:05 AM »

#### Chris_M_Thomasson

• Fractal Feline
• Posts: 175
• Programmer by trade; love fractals and math! :^)
##### Re: Natural Field Lines....
« Reply #10 on: September 14, 2021, 06:40:43 AM »

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