Mandelbrot Set and Multibrot Set Plotter (version 6.0)

This is an upgraded version of the Mandelbrot Set (M-set) plotter, with added features to plot different types of Multibrot Sets. Currently, 29 types of M-set/Multibrot Sets can be plotted.


Check out cool fractal images created with the Mandelbrot and Julia plotting tools in our Fractal Gallery! You will always find the newest creations on our Facebook page.

Quickstart:Click "Run/Re-Run Plotter" button to plot the default M-set image.
To zoom in on an area of the image, hold down the left button and drag a selection with your mouse.
On a touch-screen device, zoom in by tapping the desired point on the image.
Change the "Type of M-set" to explore 29 different Mandelbrot and Multibrot sets.
Further explore the image by changing the "Plot Size", "Max Iteration", "Hue(Color)", and "Escape Radius" options.

→ CLICK HERE TO [ SHOW ] MORE USAGE INFORMATION
Click "Run/Re-Run Plotter" button to start and display the whole M-set image.
After the initial M-set image is displayed, you can use the Mouse Left button(down-move-up) to select a specific portion of the image to zoom-in.
Or, on a "Touch Screen Device", just "touch" at any point of the image where you want to zoom-in, the image will be magnified and the touched point be placed at the center of the canvas.
The boundary of the M-set, and the areas close to the M-set boundary but outside the M-set, will exhibit great complexity and beauty. Whereas, all M-set points are colored as black and the M-set's inner structure is not revealed at present. Zooming into inner of the black area will obtain no detail, but can cost more computation power.
The Zoom-In operation can be repeated/iterated to see more details of an image area.
The "Zoom-out/Back" button can be used to reverse the Zoom-In operation step by step.
At any zoom-in stage, the user have options to:
select a larger "Max Iteration" number to increase the image resolution,
select different "Hue(Color)" algorithms to signify different aspects of image details,
select different "Escape Radius" to explore its effect on the image,
change the "Plot Size" to get a bigger-size and higher-resolution image,
use "Reset/Init" button to jump back by one step to the initial stage and displays the whole M-set image again,
or, select a different Type of M-set/Multibrot sets to start a new plot session.
In theory, the M-set/Multibrot set image zoom-In levels can be infinite, whereas the actual zoom-in levels of this plotter are limited by its accuracy. 
A fuzzy image, and/or the displayed mouse (x, y) position showing no or little change when the mouse is moving over the image, indicate the plotter has reached its accuracy limit.
r(x,y) is the distance between current mouse position and the origin point (0,0).
M-set/Multibrot sets plotting can be computation intensive. 
Combination of a large "Max Iteration" number, a large "Plot Size", and a high order(degree) Multibrot type, can trap the plotter in a lengthy calculating status. 
In this situation, if you do not want to wait, you can click on the "Restart/Reload This Web Page" link to stop the running plotter and start a new session.

Click "Run/Re-Run Plotter" Button to Start

More Information for the M-set/Multibrot set Plotter:

The M-set is generated by iteration of a simple complex equation: `z_(n+1)=z_(n)^2 + c(x,y)`

For a point c(x,y) on the complex plane, with designated iteration parameters of a maximum iteration number, a escape radius(usually 2 for M-set), and an iteration condition abs(z(n))<=escape radius:
If the iteration reaches the maximum iteration number, the c(x,y) point is defined as a member of M-set;
If during the iteration, the condition abs(z(n))<=escape radius fails, the iteration is stopped and the point is then defined as a non-M-set point.

The escape or jump iteration number, denoted as Jmp for each non-M-set point, represents the property of the point. Coloring each non-M-set point according to its Jmp value will produce a colorful and amazingly beautiful image.

This plotter provides 14 types of simple coloring/rendering algorithms and they are displayed in the Hue(Color) selection menu.
Hue(Color)=((Jmp-Min)*360)/(Max-Min)
Hue(Color)=((Jmp-Max)*250)/(Min-Max)
Hue(Color)=(Jmp/IteMax)*360
Hue(Color)=((IteMax-Jmp)/IteMax)*250
Hue(Color)=Jmp
Hue(Color)=IteMax-Jmp
Hue(Color)=((2*Jmp+10)/IteMax)*360
Hue(Color)=((Jmp/IteMax)*360)^2%360
Hue(Color)=((Jmp-Min)*120)/(Max-Min)
Hue(Color)=120+((Jmp-Min)*120)/(Max-Min)
Hue(Color)=240+((Jmp-Min)*120)/(Max-Min)
Hue(Color)=240+((Jmp-Max)*120)/(Min-Max)
Hue(Color)=120+((Jmp-Max)*120)/(Min-Max)
Hue(Color)=((Jmp-Max)*120)/(Min-Max)

Where, IteMax = "maximum iteration number".
Max = maximum of Jmp of the non-M-set points for the current/plotted image.
Min = minimum of Jmp of the non-M-set points for the current/plotted image.

Variants of M-set equation can also produce interesting images and they are also included in our plotter. 
The variants are called Multibrot sets and their equations are written as: 
`z_(n+1)=z_(n)^(m)+c(x,y)`
where m is: 3,4,5,6,7,8,9,10,,,,
or -2,-3,-4,-5,-6,-7,-8,-9,-10,,,,
and
`z_(n+1)=(z_(n)^(m)+c(x,y))^(-1)`
where m is: 2,3,4,5,6,7,8,9,10,,,,

Other 2 variant complex equations are also included.
"Burning Ship" equation:
`z_(n+1)=(abs(Re(z_(n)))-i*abs(Im(z_(n))))^2+c(x,y)`
"Tricorn" equation:
`z_(n+1)=(Re(z_(n))-i*Im(z_(n)))^2+c(x,y)`

Based on previous version of the M-set plotter, this upgraded plotter uses the offscreen technique to improve GUI responsiveness, the image process technique is used to reduce image plot time, and the multiple web worker(thread) technique is used to speed numerical computation.

Depending on the device hardware, operation system, and browser, the efficiency of multiple web workers can be limited. The reduction of calculation time may not be proportional to the increase in worker number. You can try different worker numbers to find an optimal one for your browser/device.

The following wikipedia links provide more Information for Mandelbrot set and Multibrot sets:
https://en.wikipedia.org/wiki/Mandelbrot_set
https://en.wikipedia.org/wiki/Multibrot_set