Rift II and III

[Pauldelbrot]

These images result from zooming into double scepter valley, picking a minibrot from the stem of a seahorse from quite close to the bud attachment, then pulling up an embedded Julia from near the tail of a Scepter Valley seahorse.

In the first image, the main layer has a dark red to hot pink to white gradient, logarithmically stretched over the iteration range in the image -- 75,793(!) to over 1,000,000. Overlaying it is a 75%-transparent additive distance estimator layer, with:

• dark blue further than one pixel from the M-Set
• shading logarithmically to very pale blue 1/10,000 of a pixel from the M-set and remaining
• very pale blue within 1/10,000 of a pixel of the M-Set.

This layer makes the delicate filament structures and triple-seahorse structures visible.

The second image also has two layers: one with a linear gradient map and one with a logarithmic one. The linear one shows the details of the "tapestry" surrounding the filaments and embedded Julia; the logarithmic one, which is multiplied on, makes the embedded Julia purple and brings out the detailed structure of it by shading the image's highest-iteration areas towards black. Their combined effect is that of a single gradient that shades from dark red to bright salmon to off-white to coral pink and back to dark red, repeatedly, but with a more gradual shift to purple and black.

These were slow, slow images for one this shallow. It's the high iterations: the MINIMUM iteration count in this image is 75,793! Moreover, there are some pixels that exceed a million iterations. The first one is worse because it also uses the distance estimator. It took 24 hours (more, actually, with interruptions and some sharing of the CPU with other tasks; 24 hours is what it would have taken if the machine had been devoted to calculating it without interruption or any other heavy use).

As usual, links lead to other sizes, including 2048x1536, and PNG-format images are available upon request. Note that Rift III is huge -- the 2048x1536 JPEG image at the link is 6 MB(!) and the PNG is over 8. Something about Rift III makes it compress very poorly.

Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0.

Detailed Statistics:
Names: Rift II and Rift III
Date: January 27, 2009
Fractal: Mandelbrot
Location: Embedded Scepter Valley Julia near a minibrot in Double Scepter Valley
Depth: Almost Deep (20 decimals)
Min Iterations: 75,793
Max Iterations: >1,000,000
Layers: 2
Anti-aliasing: 3x3, threshold 0.10, depth 1
Preparation time: 20 minutes
Calculation time: 24 hours (Rift II), 15 hours (Rift III) (2GHz dual-core Athlon XP)