## Into the Depths No. 612 comments

Into the Depths No. 61

Centre -0.154317638306776043979878599001907817102842227602773333333 + 1.03097537884458734193142580902824818171779774812615111111i
Width 1.288e-44
Maximum iteration 12978
Precision 160 bits
Colouring method: iteration

Posted 17 July 2013 by in Art, Fractal

### 2 responses to “Into the Depths No. 61”

1. For your iterative coloring map what’s the algorithm for your color ramp (transitions)? Do you know of good resources for a variety of color ramp algorithms?

• Saturn has two methods of editing colour maps, “manual” and “auto”. For manual editing a number of colours and their indexes in the colour map are specified, so an individual colour can be specified for every index in the map or fewer colours are specified at key indexes in the map and rest of the colours are filled in based on the gradients from one specified colour to the next. If there is no colour specified for index 0 it implied and has the colour black, the number of colours in the map is the value of the highest index (maximum value 511) plus one. For auto colour maps a waveform is specified for each colour compenent, there are three waveform types (sine, saw and parabolic), there are always 512 colours in the map and the colours are adjusted by altering the horizontal and vertical offsets, maximum value and the number of cycles of the waveform. For version 4.0.0 (still in testing) a third method of editing colour maps is added called “components”, i.e. index points can be specified for each colour component.

The colour map used here was an “auto” generated map, the “waveform” used for all three components (red, green and blue) is “parabolic”, a parabola doesn’t repeat like the sine wave so is an artificial contruct. The parabola is calculated from -1 to +1 and scaled to fit a vertical range of 0 to a maximum of 255, horizontal scaling is based on the number of cycles, in this case all components have 3 complete parabola. The waveforms all have maximum applitude (255) and start at different horizontal offsets, the red component also has a negative vertical offset which moves the waveform down and where the values become negative the sign is removed so that the waveform is reflected back on itself, for positive vertical offsets the waveform is similarly reflected back on itself. Note: amplitude for sine and saw is from negative peak to positive peak.

The inde of the colour selected from the map using the iterative method is simply the remainder of the number of iterations divided by the number of colours in the map.