# Millionaires

An occasional series of Mandelbrot set deep zooms with central period just over a million.

Explored with Mandlebrot Perturbator GTK. Rendered with Fraktaler 3. Post-processed with GNU Image Manipulation Program.

# 1 001

Millionaires 001

2023-08-30, period 1137764.

Parameter files: KFR / F3 / MP.

Inspired by Mandelbrot Deep Julia Morphing 1 by Microfractal on DeviantArt, I did fewer initial Tree morphs before starting the S/Tree evolution, and I finished on an S instead of a Tree.

# 2 002

Millionaires 002

2023-08-30, period 1774820.

Parameter files: KFR / F3 / MP.

Situated near the 1/8 child of the 1/3 bulb, spirals in groups of 5 fill the empty space between linear features extended in groups of 5, formed by alternating between length-wise and width-wise morphs.

# 3 003

Millionaires 003

2023-08-31, period 1012176.

Parameter files: KFR / F3 / MP.

Starting near my decade-old location navigating by spokes, final example a relatively shallow (zoom factor e301) embedded Julia morph is formed by zooming into the neighbouring bulb at each level, resulting in concentric rings interspersed with zigzag patterns. My normal zoom manipulations using size estimates didn’t work here, the zoom depth went up by a roughly constant e20 each morph instead of by a multiplicative factor.

# 4 004

Millionaires 004

2023-08-31, period 2206683.

Parameter files: KFR / F3 / MP.

Instead of morphing via shapes with 2-fold rotational symmetry, for this one I zoomed deeper to the 4-fold rotationally symmetric echo. Going to the end of one of the branches, extending 3 steps, and repeating, gives a sequence of periods that increase by a factor of 3 each step.

# 5 005

Millionaires 005

2023-09-01, period 426913.

Parameter files: KFR / F3 / MP.

Only 5 images in and already breaking the concept. The next stage of this one would require zooming more at the start to give an extra layer of hairs to unwrap; the extra zooming would increase the period of the penultimate layer by about 3x, pushing it beyond a million before the final layer is reached (increasing period another 2x). I chose not to redo it and instead let this one fall short of the target.

Zooming into the antenna mini of the antenna mini of … increases periods by a factor of 3 each time and adds another layer of hairs. Picking an embedded Julia set in the outer layer, morph into a tree, with the twist that at each morph, go a layer deeper in the hairs.

# 6 006

Millionaires 006

2023-10-13, period 1166862.

Parameter files: KFR / F3 / MP.

Morphing three shapes in a “rabbit” configuration. Prototyped with Inflector Gadget, the structure is formed by morphing within the shortest branch of the rabbit at each level, cycling between 3 different morphing actions.

# 7 007

Millionaires 007

2023-11-28, period 1179209.

Parameter files: KFR / F3 / MP.

Trees interleaved with lines, formed by morphing the largest shape next to the central shape at each level.

# 8 008

Millionaires 008

2023-11-28, period 1295624.

Parameter files: KFR / F3 / MP.

Similar to 006, another three shapes in a “rabbit” (lines and two kinds of trees).

# 9 009

Millionaires 009

2023-11-29, period 1541856.

Parameter files: KFR / F3 / MP.

Five kinds of shape in a 2/5 structure. Clockwise from center: connected tree, isolated tree, basilica, some messy spiral thing, line.