Page 3, More holes, spots, and dots

At this point I would like to explain that certain black/gray holes, dots, and other types of spots might actually be a feature that enhances a fractal image. I was reminded of this fact on the Ultra Fractal mailing list lately. Some artists use black quite a lot in their images, so it is actually a matter of personal taste and should not be always assumed to be a mistake that is in need of correction. That being said, I will discuss ways to remove such features in the event that it is not something that the artist wants to keep in an image. Here is one such hole that is not removable by the method I discussed on the previous page.

The reason increasing the iterations does not close this hole is because this is a convergent fractal. This happens with a Newton or Nova type of fractal. I have to admit that I do not fully understand the math involved, but I do know how to close this type of hole. It is a matter of reducing the Bailout value. The Bailout is 0.00001 by default. If you decrease it to 0.0000001, the hole is so tiny it is hardly visible. Below the picture is the upr showing the closed hole so that you can change the Bailout and see the difference it makes. If you have UF4.04 with the explore feature, you can really see the effect. Make sure that you bump the exploring range down to around to 0.07 by clicking the little magnifying glass with the + or - sign on it. Changing the exploring range is something that I do quite often, especially when I don't see any changes, or when the change is too large while in the explore mode.

Convergent1a { ::7ogjZhn2Nm5TztqNQA87Zm8dgxnanXjDsrdsT7whkcrz02Dv393oAy2qBQ8kwJP3P9dlwACQ   yO+kZ/nk2d1+jxenil1wK+9bvJKqR0UwTX8is6duaPvqJhtI6DRezh01rjjOwF7P0Y/aB7EX   pTTMelp45iGd6i/ipOF9yyovdQqqakV/xm7TWdPEHvZxt3Y9wuKZs6GhsKdxzss32rkHryXE   JrZZimTpJxx3eTJruWUtv1aabwVpxLx1ri3uNeDmks5+7on3uJe9K8hH2ksKqktvK9htLXHH   /Y8qbvZnUVesgZjQJ7nCTIoQHHVzVZH4ZvlK3tLanogXxKpjce5/u84uyFG7pFUdyK6u/W+O   7PPWIYwdfthXDLiq/umzzTSvLZZy2tbpzHtVSg4VJbPrDSjvP2EH6xPENZHMC1pVSSQt8Daj   g3T7jv/KTUIP2QnsY7nESmiXw+ZaixfRlWkzbLLKWleH5Ylsif7NkT9qy5kZUaDGMS/DVz4T   Gu8YWxCnzFe3/oeV08NFrWvodry/JlZaKl5802vSyaM6pOBtpahmknVUzpaeaWhUz1NtObkm   JLkq0chuhVlxdFu75SNvJdhRQ0TLm4Cp1uqVUFjVY0cQx1HkF5UmBWbyiyCReb4rkDezKKMl   VmpXia+oHjGeeR32vhpsp4zPfuRYZ8Qc0vJqti63VHraSTO/UyH2m+dHrySfawJwR8znlhOy   e5ssS6eE1JDpLKFV/yT/2z/qz5vTJ71ztHOCxk0nmIBS/yMfRsf57ksK9LTksO9lBHT0HYU9   Txpb9V7L6qUJ89718aWb+LNpPdYUIq4aNlFX7EGmuRJF5td0xLfY0nN9ZP278ShSJV6zdv9B   YvSkbr85C2eZVbt3oYni/jj8qsTJubDWZNVvPmztSdiT9BmmEOUAHCA4NAQa88AAuBomTTE1   prGk0Yqs2swqR+egT9XKZT6q1DGbFqF/H3d5bF+G/D6m0oQw01UtYohjSHlcqNd0RqT409uw   MpuhuxS5WTX7gHtaopcm7ex3PkcYUKfcQMi8bot+wyzdMufe8K4hNPmYG/FngbGK5tGUKfnr   HdfNJXJ2NaFM5NnzI9omGyOZzZTZrecZSC4Kqzyen51cWj2QRq2PJEt66243PxH7tgpewoEe   hT06PcyKTcUisALl1RPLlVuNd+GrgLyl6MZt71huJn9zxLobdM1U110wxMKCTuE0rWqb613p   0cxbfnFjrJ00XiT8aBfYAkR2RNnpNeIppnTd4sczY2mTkntntAGo4V7pXfY8udkN95fvaHSl   j93uDpOTLV0RuVkvMUvuG2eeqoskepFWDv4kjBt5eCE1NekeFC14Y45eCh3mmxJZvKY6p3zo   tw5L7jM1XGwKzQr8clobFPra9U3syxNjinkOPmbk4440O+GGZqug6MnV1tSdIE2XbJZqBtHF   M2jv8C+7tuizWNPFMolTVLFVdvLCEiRB9MqRTnhPFjCCzogQMKwLjCCxogZMKwLjCcYUeCgL   jCmxogAMKwHjC8xogQMKYWbL4jSBBoUQQKFEgSBzpUgXKF4Sp6kp400BaSow2m42IDzmMDjx   V9nkOWljvjxVgDuqvl1k6Gvr9wqgZsqxK8NyDmwq6FPFU5eW9xqG7o/lyPraoI7FU5EAfsqZ   6cBVO+OlV1XndAVuNFzYVOa8DqG79gNvzUC7i+o710rTzgLSzgrSzgA0M4C0M4a0M460MwHN   D8QzAv0MwHND8QzgLTzgA0MIEND8TzAP0MwLNDuGNDCTzgLQzgLQzw50MMEND9TzwPFNDDTz   wQ0M0LNDDRzwZ0M0LNDDRzwZ0McGNDDQzQf0M0HNDDRzwZttoPaGGgmhBpZYAaGOnmhepZoH   aGGmmhzoZoXaG6hmhjpZ4caGOnmheoZYIaGGmmh+pZ4FoZ4loZYYaGeZaGeVaGeBaGeFaGGg   mh+pZYQaG+JoZ4VpZ4ngmhXkmhXlmhBoZ4FoZ41oZ41pZoPaG6hmhepZoPaG6hmhXmmhBoZY   IaG6nmheoZoXaGeNaGGmmhXgmheoZ7N9cURv9HmXS1pKzv7/XF0geeEp9k14oO7WuIiuO9GP   P9EXHpLlSqdj+qxdagzZw32kIRVO/npPG1+r8m8wmNbgk1nFjb3eWBtFO//EY3BDB0f06+PF   g1uhyR6t38/A2gXlmD== }

Next, there is the occurance of numerous tiny black dots when there is no central black hole and the inside percentage is 0.0 when you look at the Statistics window. In this case, it is still a matter of Maximum iterations. If you raise the value up just slightly (from 250 to 500), you will see all the tiny black dots disappear. Below is a before and after picture.

Before

After

Here is the upr so that you can see how these little black dots appear before and you can change the Maximum iterations yourself and see the difference it makes. blackdots { ; Copyright © 2007 by Mary C. Thornton. fractal:   title="blackdots" width=550 height=410 layers=1   credits="Mary C. Thornton;7/14/2007" layer:   method=multipass caption="Background" opacity=100 mapping:   center=0.396892241197/0.332274028473 magn=4.7877275 formula:   maxiter=250 percheck=off filename="Standard.ufm" entry="Julia"   p_seed=0.3571889/0.0878836 p_power=2/0 p_bailout=1e20 inside:   transfer=none outside:   transfer=sqrt solid=4288282714 filename="ldm.ucl"   entry="ldm-Doodads" p_trp=yes p_txp=yes p_m=3 p_mr=B p_mrf=no   p_tad=0.0 p_fm=1/1 p_cm="Min Distance" p_mc=8.0 p_tm=1 p_ta=0.0   p_change=1 p_exp1=1/0 p_exp3=1/0 p_exp2=1/0 p_tw=0/0 p_tw2=0/0   p_tw3=0/0 p_op=+ p_ptt=" Off" p_pta=0.2 p_pct=no p_nsc=1/1 p_ur=no   p_v2=1.0 p_tb=15 p_f=1.05 p_step=20 p_r=0.0 p_pto=-1/.75 p_psc=5.0   p_ptd=5.0 p_ptm=1.0 p_pff=1.0 p_tp=1.0 p_sk=0.0 p_co=no p_pwr=3.0   p_mul=3.0 p_sb=0.0 p_sa=0.0 p_msk=0.0 p_im=no f_fn4=ident   f_fn1=ident f_fn2=ident f_fn3=ident f_fn9=ident f_fn8=ident   f_nufunc=ident f_nufunc2=ident f_nufunc3=ident f_fn5=ident   f_fn6=ident f_fn7=ident gradient:   linked=yes smooth=no rotation=-200 index=96 color=16777215 index=263   color=0 opacity:   smooth=no rotation=-200 index=96 opacity=255 index=263 opacity=255 }

On the next page we will look at other types of extraneous features, which I usually call debris, and how to eliminate them.                                                                                                Page  4