Exploring the depths of infinity

The most distant known galaxy (JADES-GS-z14-0) is estimated to be 33.6 billion (33.6e+9) light years away.

Within an atom is an electron with an estimated diameter of about 5.6358806454e-15 meters.

For comparison an electron diameter is about 1.773334571907762e-41 the distance to the farthest known galaxy.

These numbers are estimates expressed in floating point format with up to 16 digits of accuracy for the mantissa (the number before the ‘e’) followed by the exponent (the number after the ‘e’). If the distance comparison value of 1.773334571907762e-41 was to be expressed accurately in decimal digits it would require 41 decimal digits to be displayed. This would be a 1 followed by a decimal point and 41 digits.

Fractal calculations require accurate numbers not estimated values. Without an accurate number, calculations would not be repeatable and transition edges would be fuzzy at best. Traditional floating point numbers used by computers and calculators have a maximum mantissa of 16 digits (7 digits for a GPU) which prohibits the accuracy required for fractal calculations at resolutions exceeding 1e-15.

Fractal Echo goes beyond traditional floating point values to deliver an incredible 1e-306 accuracy. This is 306 digits of accuracy which would be written as a 1 followed by a decimal point and 306 digits. The result is an accurate and repeatable number that can be used for fractal creations without fuzzy edges.

To demonstrate of the accuracy Fractal Echo delivers, consider that the relative distance estimate of 1.773334571907762e-41 used to compare the diameter of en electron to the distance of the farthest known galaxy would fall short of the 1e-306 accuracy delivered by Fractal Echo by a factor of about 1e265. This would be a number with a 1 followed by 265 digits which is a massive number.

Fractal Echo uses an extremely large and accurate number to create and visualize fractals. The benefit in using an such an extreme and accurate number enables Fractal Echo to create fractals to levels never before seen. This accuracy enables repeatability in creating fractals that can be bookmarked, shared and recreated.

It should be noted that most persons will never in their life encounter, use or require a number exceeding 16 digits of accuracy especially in real time. Even calculators are generally limited to 16 digits of accuracy. That Fractal Echo can reach accuracies of 1e-306 in real time is an incredible feat on it’s own. In addition to the 1e-306 accuracy is that Fractal Echo offers search depths up to an incredible 100,000,000 iterations.