Editing Mandelbrot set (section)

===Inner structure===
While the Mandelbrot set is typically rendered showing outside boundary detail, structure within the bounded set can also be revealed.<ref>{{Cite journal |last=Hooper |first=Kenneth J. |date=1991-01-01 |title=A note on some internal structures of the Mandelbrot Set |url=https://www.sciencedirect.com/science/article/abs/pii/009784939190082S |journal=Computers & Graphics |volume=15 |issue=2 |pages=295–297 |doi=10.1016/0097-8493(91)90082-S |issn=0097-8493}}</ref><ref>{{Cite web |last=Cunningham |first=Adam |date=December 20, 2013 |title=Displaying the Internal Structure of the Mandelbrot Set |url=https://www.acsu.buffalo.edu/~adamcunn/downloads/MandelbrotSet.pdf}}</ref><ref>{{Cite journal |last=Youvan |first=Douglas C |date=2024 |title=Shades Within: Exploring the Mandelbrot Set Through Grayscale Variations |url=https://rgdoi.net/10.13140/RG.2.2.24445.74727 |journal=Pre-print |doi=10.13140/RG.2.2.24445.74727}}</ref> For example, while calculating whether or not a given c value is bound or unbound, while it remains bound, the maximum value that this number reaches can be compared to the c value at that location. If the sum of squares method is used, the calculated number would be max:(real^2 + imaginary^2) − c:(real^2 + imaginary^2).{{Citation needed|date=March 2025}} The magnitude of this calculation can be rendered as a value on a gradient.

This produces results like the following, gradients with distinct edges and contours as the boundaries are approached. The animations serve to highlight the gradient boundaries.

<gallery mode=packed heights=160>
File:Mandelbrot full gradient.gif|Animated gradient structure inside the Mandelbrot set
File:Mandelbrot inner gradient.gif|Animated gradient structure inside the Mandelbrot set, detail
File:Mandelbrot gradient iterations.gif|Rendering of progressive iterations from 285 to approximately 200,000 with corresponding bounded gradients animated
File:Mandelbrot gradient iterations thumb.gif|Thumbnail for gradient in progressive iterations
</gallery>