From 2a12e1c87af8f2be0fa0c8451f1751b3a540057d Mon Sep 17 00:00:00 2001 From: Sven Riwoldt Date: Wed, 7 Jan 2026 20:12:57 +0100 Subject: [PATCH] Newton --- Newton.py | 58 +++++++++++++++++++++++++++++++++++++++++++++ newton_fractal.png | Bin 0 -> 93549 bytes 2 files changed, 58 insertions(+) create mode 100644 Newton.py create mode 100644 newton_fractal.png diff --git a/Newton.py b/Newton.py new file mode 100644 index 0000000..a3f3f38 --- /dev/null +++ b/Newton.py @@ -0,0 +1,58 @@ +import math +from PIL import Image + +width, height = 800, 800 +max_iter = 40 +tolerance = 0.001 # Wie nah müssen wir an der Nullstelle sein? + +# Die drei Nullstellen von z^3 - 1 = 0 +roots = [ + complex(1, 0), + complex(-0.5, math.sqrt(3) / 2), + complex(-0.5, -math.sqrt(3) / 2) +] + +# Farben für die drei Nullstellen (Rot, Grün, Blau) +root_colors = [ + (255, 0, 0), + (0, 255, 0), + (0, 0, 255) +] + +img = Image.new('RGB', (width, height), (0, 0, 0)) +pixels = img.load() + +for py in range(height): + for px in range(width): + # Koordinaten umrechnen (von -2 bis 2) + zx = -2.0 + (px / width) * 4.0 + zy = -2.0 + (py / height) * 4.0 + z = complex(zx, zy) + + found = False + for n in range(max_iter): + if abs(z) < 0.000001: break # Vermeidung von Division durch Null + + # Newton-Schritt für f(z) = z^3 - 1 + # Formel: z = z - f(z) / f'(z) => z = z - (z^3 - 1) / (3 * z^2) + z_next = z - (z ** 3 - 1) / (3 * z ** 2) + + # Prüfen, ob wir nah genug an einer der Wurzeln sind + for i, root in enumerate(roots): + diff = z_next - root + if abs(diff) < tolerance: + # Farbe basierend auf der Wurzel, Helligkeit basierend auf Iterationen + brightness = int(255 * (1 - n / max_iter)) + r, g, b = root_colors[i] + pixels[px, py] = ( + int(r * (brightness / 255)), + int(g * (brightness / 255)), + int(b * (brightness / 255)) + ) + found = True + break + if found: break + z = z_next + +img.save("newton_fractal.png") +img.show() \ No newline at end of file diff --git a/newton_fractal.png b/newton_fractal.png new file mode 100644 index 0000000000000000000000000000000000000000..e0cf3ecaeb6cde86d48b802dd53ae61da25dc846 GIT binary patch literal 93549 zcmX`SRa{%m_dSdScN*NS5L}D96^8=B0>O$?+={!q75Cy!aY%5t0tJdwT-xHaK;Jyy z-~aPooSSnob7s$;*=w)0POP@3G9ET1HWCsN-dhy~T_hw_`u`qG6vP`n;#6rQWF(}w z3bJ~>`RC7EIr|3P+_>8lLfINM+L4|rl(*C=xU2SQ>?wRFRw-O5T#L%Z9V(xe_^PaQ zi$Xg>wTOPA1jTp8c%uet2qJGG2jz(%3o&d`sbl2ZU+Ke6Soz$Er~<#WW-;@e&0P&R zN!}lLnzjUGWtF$PNJ`&dWBm$-j{~rKT#&55Ij-N1+M~yM#J|2hWz~2e?2jac#DsCH z48tTxLFW#AeY0G%OD=*EXQ@IJyZkfMxGeI0A8Nj@vJze(ae?{A_` z=lIOzlO`@yFToHwoLe!PGt39h&75lCps;w#2A+lP(oH#P&C-;%O&cKC^M(X^gL0eA zRU8z1r*D#9J790&ot^qI(XqLE+21xs@Z;8ftiuUw;2;_Y-T02i)G90g6cRpqIyGTk zeG`YtPl|a?*!jJ7VGLcA43Nw7lsj0A_ze3C+6D0g@x#I(2NEl7U~;nbjv^J0<1sQF zm);Kx&^EHP6h=QPtyqBUKX72y{wm!f#;~ z^m&1K>|sJl=3^{u5WCC&rvkze}4w`=T*zn9iBg9K z*X#|pS-aKxtR=FxJ0{s*XJpD2cBW<_k3&5#U5ybC9NE}=7u{nKru0q(ZH}W;v}gFD z%!sbM`>XX3P}$Tb`0~j!u*cFGW4eJnAo`blwyX+jQrj-B;!XNf%t687^gPS4N-ZwY zRuEc1%DHM#((u?n0he)(;l?sm2pPe&Du{m73X*nIT5BQ&vKod`%L8Pg}i8!vv$eF9aJb9pBL|8s>XOIF3pky zp}8BL;2sP|ZsizV^ugbjz=&;+ht{hMDtuIO)h5{R$gbM#rT@Mn5T2t3{_N#U!j&1omfElxA#l@pq2fpia?rGYNC z>R!bgXm@ldx1Q}g>#;|=L5+wf(tq(>eP=z7)M`F%jPZUlfMsIrS+wR&6EyD&!%}_u z`VnDOs=u5_x{FKked&yb_Fk^zSS}D)5Ja?=>>GI`vs?7*YQPMMXCN@Ns3NIatA^30 z{R_$R>{^)kCy`Ik3-SL#m&15Y!|KOk=uy_Fls(@Mn9QQ5p;P$LJ&anM-m8x>dQ_Nd zg=Lo6zj-2R5LTvLk=XzB7wy9%R$<@kXD(?fU7JL=sAm0Xa9)gqdCxA$aaA*YRk8Ei z_)g%|s-yLM#N6sTw0h~58oX+sLL_sXT$auE5p$vYAY)|j_PvWvY$mL_Pc0M~3=c08 zXUZO(&gG8|9#HT0TE0ty?_z{j7dx>j%?!R>TDYTWhqZ1Gb0ji8?@?2K7?*dyoz!(E zdMwn=VND~Sso+na+5T;{1KzpCSs4CzFBv5MG4{8Q@1wQw5btwJpVBq3wU$QnlM{Sh zx#?4AbL7VaxFHSqhZC9C**gp8T&!!d6-+-na%l?mkAfLfpU&h=x%|?R0{%g-albv> z-A2}~{yKlt6`oG#=Jp(B+4>_lb^SL-*qZ*RvLLJBM~uQpa+98~5AUt&T>4ABYL3%3 z^r7O-mZ2&7TmJjsfg@1oC%0+di zII{t-$y$6?whe1n9$yNa8Yg%do#J9W<2CnN*nXkDB+H>F(aLn~mm(64+|}zT@Bl2A z9mSh08+Q(lq-V>Vt+eYudU;p=Qz58&qAuBDL%AKzu&URrH@J7N+*mHeCym4vjIyD; z1BegklZz^Qn|%>Tnn0cqIoH*iZ5zqaNV ziOshE6-mB@!sGTfqFTSm%@(A3TME+TcvZ*a^D88t!?a@^2NdMYmcV(?aOaiMg9(C|Z8cM$bl!=j#Bl04<+-H%EPV`-Ec zyIuv1Y_Q$8&y*w#4AEz;~0+>tg})&CAV_yhs+eKlwotny)LoqEB)m5as-?XaL|t&hz)jKc&3~6 zMU=%4YR=TmB5vbc2!Psg>uP)C9|wdg(@GD;{UTn~zoDatX)ROznaLYa8)&t%PU{F7 zb}~iEB~|Xz$np;Be~4ZmPvD+}{Io zNfH&w%!d3M6v8i8=Z>`_ZtCOeaoIA+ z#KO%^z(F^`$M#ZXEZDggWu@-OF!rf2tzOYS>vJ2l8icD*?_}Xo zYmO2rAoxKsJ-yiFUwW}6k4>?G+=MKP;Duiz{=FL2g>lEBQg!5-k;Nuy-QLTbF2I_` z2|h{R68xQ)oH(G77PRQ0Pz2fhKHn1tnV=T;^GFDZJMdex<}X%@N+x=a5KAAxR6LCTh<@Y)&}j0VP~`UMp8>$M?&7vOCrX{{_Bod z3Fx68kG_aT?x}nuk93d%g_1MievO8(P9`Va5rOby*JHgG8Jg|*K{V@wp~PGHv{p&!T(RCPtR#9Z&9 zEP%r5P2M7Ez@}g*j)78B@*9HilCYn<`SeL2fzVZ6ZcoqRd$zQ&nM*ZQuBg4Uz9IU|>e$IXqQ!I^k@ z_D{wl;;psLVOR#FFaeT%UYL*jEMK!LUQb+MROlsQ_&Yb`H~9YZq2_Mu{%!Tx!>Q*r z>(OhnctQ&k-zmy)4Qd70Y5+T#7+x{TN1cR)b2$30eK9yK zwHhf&r!9i+*s*$+7Y&b*pEd9D*+TtJ0HYiN5vczu^F)4X-E+Ji6E%P9ftK+XR!*QH zb;1Jxfzu(cc%L?C7m&PhWtf#IGLj2fj2z0 z%=nX4Y5ySm1(kinRk7EWY@PltOf}+0`~|bup+x_+POUvnvEb`hQUnX1@X{qB#$1+i z^b0808JW)C{9xR;QqYIVhC(95;h~#~xJt|qQqsO?ZPUs59BrO+B|uh|uPjWS4se@z zGU@~?aN5X3%gifgv(%Q~Blw=G5Zt3*GZnPEUUH-CRJWu?O

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