Fractal Dragons

These images and roots are from the Mandelbrot set function: zn+1 = zn2 - c

Root search and images generated by custom software using 512 bit fixed point math (approx. 149 decimal digits).
This supports resolving atom domains thru at least period 80.
Using a new automated adaptive search algorithm the number of roots found has increased dramatically.
Roots with designations (2,669 Roots) - These are the bulbs on the main body.
To reduce the file sizes only the upper half plane roots are included in the following files. For each non-real root there is a coresponding complex conjugate root implied.
NOTE: A bug in the fixed point text output corrupted some least significant digits in previous files, this has been fixed and new files uploaded.

Root Status (9,157,287 Roots)
PeriodRoots FoundMissingData File
11CompleteMRoots_01.txt
21CompleteMRoots_02.txt
33CompleteMRoots_03.txt
46CompleteMRoots_04.txt
515CompleteMRoots_05.txt
627CompleteMRoots_06.txt
763CompleteMRoots_07.txt
8120CompleteMRoots_08.txt
9252CompleteMRoots_09.txt
10495CompleteMRoots_10.txt
111,023CompleteMRoots_11.txt
122,010CompleteMRoots_12.txt
134,095CompleteMRoots_13.txt
148,127CompleteMRoots_14.txt
1516,365CompleteMRoots_15.txt (1.1MB)
1632,640CompleteMRoots_16.txt (2.2MB)
1765,535CompleteMRoots_17.txt (4.5MB) or MRoots_17.zip (1.7MB)
18130,788CompleteMRoots_18.txt (8.9MB) or MRoots_18.zip (3.4MB)
19262,143CompleteMRoots_19.txt (17.8MB) or MRoots_19.zip (6.8MB)
20523,770CompleteMRoots_20.txt (35.4MB) or MRoots_20.zip (13.5MB)
211,048,509CompleteMRoots_21.txt (70.8MB) or MRoots_21.zip (26.9MB)
22576,2791,519,848MRoots_22.txt (37.6MB) or MRoots_22.zip (15.0MB)
23119,6854,074,618MRoots_23.txt (7.7MB) or MRoots_23.zip (3.2MB)
24138,5118,247,929MRoots_24.txt (9.0MB) or MRoots_24.zip (3.7MB)
25166,85016,610,350MRoots_25.txt (10.8MB) or MRoots_25.zip (4.4MB)
26169,49733,380,838MRoots_26.txt (11.0MB) or MRoots_26.zip (4.5MB)
27194,96566,913,643MRoots_27.txt (12.6MB) or MRoots_27.zip (5.1MB)
28222,456133,987,074MRoots_28.txt (14.4MB) or MRoots_28.zip (5.9MB)
29249,204268,186,251MRoots_29.txt (16.1MB) or MRoots_29.zip (6.6MB)
30279,787536,574,218MRoots_30.txt (18.1MB) or MRoots_30.zip (7.4MB)
31307,9331,073,433,890MRoots_31.txt (19.9MB) or MRoots_31.zip (8.1MB)
32339,3782,147,111,502MRoots_32.txt (21.9MB) or MRoots_32.zip (8.9MB)
33370,2134,294,596,056MRoots_33.txt (23.9MB) or MRoots_33.zip (9.7MB)
34401,9068,589,467,149MRoots_34.txt (25.9MB) or MRoots_34.zip (10.6MB)
35179,98017,179,689,125MRoots_35.txt (11.6MB) or MRoots_35.zip (4.8MB)
36190,78434,359,414,496MRoots_36.txt (12.3MB) or MRoots_36.zip (5.0MB)
37202,63268,719,274,103MRoots_37.txt (13.1MB) or MRoots_37.zip (5.3MB)
38209,436137,438,481,891MRoots_38.txt (13.5MB) or MRoots_38.zip (5.5MB)
39224,527274,877,678,318MRoots_39.txt (14.5MB) or MRoots_39.zip (5.9MB)
40230,923549,755,058,557MRoots_40.txt (14.9MB) or MRoots_40.zip (6.1MB)
41246,7011,099,511,381,074MRoots_41.txt (15.9MB) or MRoots_41.zip (6.5MB)
42253,6532,199,021,945,168MRoots_42.txt (16.4MB) or MRoots_42.zip (6.7MB)
43269,3904,398,046,241,713MRoots_43.txt (17.4MB) or MRoots_43.zip (7.1MB)
44273,7268,796,090,651,324MRoots_44.txt (17.6MB) or MRoots_44.zip (7.2MB)
45290,67317,592,185,737,107MRoots_45.txt (18.7MB) or MRoots_45.zip (7.6MB)
46294,25535,184,367,600,272MRoots_46.txt (19.0MB) or MRoots_46.zip (7.7MB)
47314,38970,368,743,863,274MRoots_47.txt (20.3MB) or MRoots_47.zip (8.3MB)
48324,947140,737,479,609,133MRoots_48.txt (21.0MB) or MRoots_48.zip (8.5MB)
494,271281,474,976,706,321MRoots_49.txt
506,308562,949,936,637,292MRoots_50.txt
51481,125,899,906,777,037MRoots_51.txt
52512,251,799,780,130,759MRoots_52.txt
53644,503,599,627,370,431MRoots_53.txt
541,7949,007,199,187,499,518MRoots_54.txt
554018,014,398,509,480,905MRoots_55.txt
563536,028,796,884,746,085MRoots_56.txt
574772,057,594,037,665,742MRoots_57.txt
5857144,115,187,807,420,358MRoots_58.txt
5953288,230,376,151,711,690MRoots_59.txt
6060576,460,751,766,026,730MRoots_60.txt
61451,152,921,504,606,846,930MRoots_61.txt
62552,305,843,008,139,952,072MRoots_62.txt
63614,611,686,018,426,339,015MRoots_63.txt
645,6309,223,372,034,707,286,530MRoots_64.txt

Searching is performed using a quadtree subdivision of the grid which increases search resolution in areas of higher root density. Within a search area first a map of the function magnitude is made at moderate resolution, then points of local minimum are refined using 512 bit fixed point math. Root searching requires twice the precision of the desired result due to squares of small numbers. As roots are added the quadtree is subdivided further and the search continues. Only the upper half plane is searched due to symmetry.
Root searches from period 22 and above were performed using a purposely limited quadtree depth. Periods from 49 and above have only been searched in selected areas.


16000x16000 Version (Use Save As, May be too big for Browser)

Period 2

Period 3

Period 4

Period 5

Period 6

Period 7

Period 8

Period 9

Period 10

Period 15

Period 25

Period 36

Period 45