# Project Day Three: Indra’s Promise

The net of the great god Indra was said to span all of space, finer than silk, and strung with pearls reflecting each other and all others along the infinite reach of the net at once forever.

Thus seemingly was foretold in Buddhist scripture the vision of Felix Klein, and the mathematical constructions used in the fractal type of this post, as paraphrased from the book, ‘Indra’s Pearls.’

Good evening, and welcome to the launch of the first weekday of this project’s posts, my attempt to more fully explore this sometimes cross but rewarding fractal type based on the mathematics of the interaction of spirals and the objects it leads to.

Today I’ve got four images to show, what I think to be the very best from today and last night generated by my current favorite app, Ultra Fractal over a period of several hours.

This on was made using my first parameter file created for this series (I generated ten such files, adjusted as needed), using an extremely well-designed coloring algorithm, ‘Double Cusp’ Kleinian group settinmgs and a rather fortuitous combination of color gradient settings.

This one uses a figure altered threefold with a kaleidoscopic transformation, using a different coloring algorithm and different but still striking gradient settings. I like to randomize and shift gradients around when coloring these, just to see what I’ll get, though the app certainly allow easy non-random color adjustments as well.

This one used my second file created, and used a different coloring algorithm than the previous two and different Kleinian groups (Schottky bubbles) to generate this image. Of today’s pieces, it took the longest to render, but was well-worth it I think.

The scope and potential of this fractal type is amazing, despite the relatively simple starting idea of interacting spirals, or perhaps even because of it. I’ll include further images tomorrow, and may you all fare well the remainder of this week.

Talotaa frang.

I seek to learn through this site and others how to better my ability as a person and my skill at using my reason and understanding to best effect. I do fractal artwork as a hobby, and I'm working to develop it to professional levels, though I've a bit to go till I reach that degree of skill! This is a crazy world we're in, but maybe I can do a little, if only that, to make it a bit more sane than it otherwise would be.

Posted on Monday, 20:35, October 28, 2013, in Fractals and tagged , , , . Bookmark the permalink. 3 Comments.

1. John Seymour

Beautiful Apollonian Gaskets, would you be willing to release the parameters for the first image ?

Sorry, I reposted the comment as there was a typo in my address…

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• Certainly! I’ll post them for you this evening.

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• Here are the parameters I used for the first image, save the gradient colors – those were randomized. Good fractaling!

Image Tab (Fractal Properties)
Width: 480 pixels
Height 480 pixels
Resolution: 300

Location Tab (Layer Properties)
Center (Re): 0
Center (Im): 0
Magnification: 1.5
Rotation Angle: 0
Stretch (X/Y): 1
Skew Angle: 0
Left Top (Re): -1.333333333
Left Top (Im): 1.333333333
Right Top (Re): 1.333333333
Right Top (Im): 1.333333333
Right Bottom (Re): 1.333333333
Right Bottom (Im): -1.333333333

Formula Tab (Layer Properties):
Formula Type: Indra’s Promise (Public Formula file reb.ufm)
Drawing Method: Guessing
Periodicity Checking: Off
Maximum Iterations: 511
Calc as slope: Checked
Max Iters: 100
Smallest Circle: 0.001
Max circle size: 0.6
Min display level: 0
Group Type: Double Cusp
Cusp: 1/15
Cusp view: Alternate
Height Transfer: linear
Height Pre-Scale: 0.4
Height Post-Scale: 0.025
Fill Type: quartic 4
Power: 2
alpha: 1
beta: 1
gamma: 1

Outside Tab (coloring algorithms; Layer Properties)
Coloring algorithm type: Kleinian Group Raytrace (Public File: reb.ucl)
Color Density: 1
Transfer Function: Log
solid background?: Checked
Apply Mapping: Checked
Group: Double Cusp
Cusp: 1/15
Cusp view: Alternate
Max Iters: 100
Smallest Circle: 0.001
Smallest View Circle: 0.001
Largest Circle: 0.6
All other settings as-is

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