Fractal Related Discussion > Fractal Mathematics And New Theories

Jeff Berkeley Formula collection

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3DickUlus:
Stumbled across this and thought it might be interesting to share here... unless it's here some where already :skeptical:

--- Quote ---http://www.lifesmith.com/formulas.html

JEFF BERKELEY, M.S.

For me, the single most interesting aspect of doing mathematical fractal art is to create and explore new
complex algebraic expressions which generate imagery never before seen by human eyes. I cannot tell you how many
nights I spent calculating and devising and generating new expressions and imagery...so much sleep was lost (however
voluntarily) since I started in 1988...

Nearly all of the people doing fractal art now, and there are thousands, use canned software which employ someone else's
algorithms...and that is fine, for a far fewer number of people have the appreciation for art as well as the technical know-how
to do their own math...

The explorer in me pushes me onward...listed here are the 700+ fractal expressions, functions of a complex number z and a
complex constant c, that were used in all of my work prior to 2004, plus all of the newer equations I devised these past few years.

Because writing some of these expressions in html (at least the version I use) is rather cumbersome, I have not written functions
for recent fractals until now. Starting at equation 1001, which signifies the year's images from 2013, I have tried to show just
how complex the mathematics is...the depth to which my exploration has taken me.

Feel free to use and re-use them to your heart's (and mind's) content.

Notes:
X is the real part of Z
Y is the imaginary part of Z
A is the real part of C
B is the imaginary part of C.

Fomulae:

--- Code: ---1--F(Z) = Z² + C

2--F(Z) = Z³ + C

3--F(Z) = (Z² + C) / (Z - C)

4--F(Z) = Z² - Z + C

5--F(Z) = Z³ - Z² + Z + C

6--F(Z) = (1 + C)Z - CZ²

7--F(Z) = Z³ / (1 + CZ²)

8--F(Z) = (Z - 1)(Z + .5)(Z² - 1) + C

9--F(Z) = (Z² + 1 + C) / (Z² - 1 - C)

10--F(Z) = Z^1.5 + C

11--F(Z) = exp(Z)-C

12--F(Z) = Z - 1 + C*exp(-Z)

13--F(Z) = C * Z - 1 + C * exp(-Z)

14--F(Z) = (4 * Z⁵ + C) / 5 * Z⁴

15--F(Z) = (6 * Z⁷ + C) / 7 * Z⁶

16--F(Z) = Z² * exp(-Z) + C

17--F(Z) = Z² * Z^(-2) + C

18--F(Z) = Z * exp(-Z) + C

19--F(Z) = C * exp(-Z) + Z²

20--F(Z) = Z³ + Z + C

21--F(Z) = Z⁴ + Z + C

22--F(Z) = Z⁴ + C * Z² + C

23--F(Z) = Z² * sin(X) + C * Z * cos(Y) + C

24--F(Z) = 2^Z * C * Z²

25--F(Z) = Z⁵ - Z³ + Z + C

26--F(Z) = (Z² + C)² + Z + C

27--F(Z) = (Z + sin(Z))² + C

28--F(Z) = C * exp(Z)

29--F(Z) = Z² + C³

30--F(Z) = C * exp(C * Z)

31--F(Z) = Z² * cos(X) + C * Z * sin(Y) + C

32--F(Z) = C * Z² + Z * C²

33--F(Z) = exp(cos(C * Z))

34--F(Z) =(1 + Jo(X))² + (Jo(Y) + C)² (Here Jo represents the Bessel function)

35--F(Z) = C * (sin(Z) + cos(Z))

36--F(Z) = Z^(-.5) + C

37--F(Z) = C * Z * (1 - Z)

38--F(Z) = C² * Z * (1 - Z)

39--F(Z) = ((Z²+C)²)/(Z-C)

40--F(Z) = (Z + sin(Z))² + Z^-.5 + C

41--F(Z) = C*(sin(Z) + cos(Z))*(Z³+Z+C)

42--F(Z) = C*exp(Z) * exp(cos(C) * Z)

43--F(Z) = (Z³+Z+C)*C*(sin(Z) + cos(Z))

44--F(Z) = ((1+C)Z-CZ²)*((Z+sin(Z))²+C)

45--F(Z) = Z² + Z^1.5 + C

46--F(Z) = Z² + Z*exp(Z) + C

47--F(Z) = (Z+sin(Z))²+C*exp(-Z)+Z²+C

48--F(Z) = ((Z³)/(1+C*Z²))+exp(Z)-C

49--F(Z) = (Z²*sin(X) + C*Z*(Y) + (Z²*cos(X)+C*Z*sin(Y)+C

50--F(Z) = (Z+sin(Z))²+C*exp(Z)+C

51-- F(Z) = Z² + 1/Z + C

52-- F(Z) = (Z³ + C) / Z

53-- F(Z) = (Z³ + C) / Z²

54-- F(Z) = ((Z+1)² + C) / Z

55-- F(Z) = (Z + C)² + (Z + C)*

56-- F(Z) = (Z + C)³ - (Z + C)²

57-- F(Z) = (Z³ - Z²)² + C

58-- F(Z) = (Z² - Z)² + C

59-- F(Z) = (Z + log Z)² + C

60-- F(Z) = (Z - sqrt(Z))² + C

61-- F(Z) = (Z + sqrt(Z))² + C

62-- F(Z) = Z²exp(Z) - Zexp(Z) + C

63-- F(Z) = (exp(CZ) + C)²

64-- F(Z) = Z * exp(X/Y) + C

65-- F(Z) = exp(X²*Y²) + Y + C

66-- F(Z) = exp(X)*(X-A) + exp(Y)*(Y-b)i

67-- F(Z) = X²*exp(Y+b) + iAexp(Y+b)

68-- F(Z) = (A-X²+Y²)exp(b+X²-Y²) + i(b+X²-Y²)exp(A-X²+Y²)

69-- F(Z) = [(2X-Y²+A)/(2X²+Y-b)] + i[(2X²+Y-A)/(2X-Y²+b)]

70-- F(Z) = [(X²+Y²+A)/cos(X²+Y²)] + i[(X²+Y²+b)/sin(X²+Y²)]

71-- F(Z) = Z⁵ + C

72-- F(Z) = Z⁶ + C

73-- F(Z) = Z⁷ + C

74-- F(Z) = (3Z⁴ + C) / 4Z³

75-- F(Z) = (2Z³ + C) / 3Z²

76-- F(Z) = Z⁵ + CZ³ + C

77-- F(Z) = Z⁶ + CZ⁴ + CZ² + C

78-- F(Z) = Z⁸ + C

79-- F(Z) = Z⁹ + C

80-- F(Z) = Z⁸ + CZ⁴ + CZ² + C

81-- F(Z) = Z⁹ - CZ⁶ + CZ³ + C

82-- F(Z) = (Z⁴ + C) / (Z - C)

83-- F(Z) = (Z³ + Z + C) / (Z² - Z - C)

84-- F(Z) = (Z³ + Z + C) / (Z - C)

85-- F(Z) = (Z³ + Z + C) / Z

86-- X = X²+XY+A ; Y = Y²-XY+B

87-- X = X³-(X²)Y+XY²-XY+A; Y = Y³-XY²+(X²)Y+XY+B

88-- X = (X²)sin Y + A ; Y = (Y²)cos X + B

89-- X = X⁴-3X³+3X²(Y²)+A ; Y = Y⁴+3XY³-3X²(Y²)

90-- X = X²(1+exp(-Y))+A ; Y = Y²(1+exp(-X)+B

91-- F(Z) = C(Z² + 1)² / Z(Z² -1)

92-- F(Z) = CZ²

93-- F(Z) = CZ³

94-- F(Z) = CZ⁴

95-- F(Z) = C*cos(Z)

96-- F(Z) = C*sin(Z)

97-- F(Z) = CZ*log Z

98-- F(Z) = C*tan Z

99-- F(Z) = C*exp(CZ) / (exp(C) - 1)

100-- F(Z) = C*exp(Z)*sqrt(Z) /n

101 -- F(Z) = (Z²(1+Z²))/(Z+C)

102 -- F(Z) = Z(1+Z²)/(Z+C)

103 -- F(Z) = (Z⁵+C)/(Z³+Z²+Z+1)

104 -- F(Z) = (Z³+C)/3Z²

105 -- F(Z) = (Z³+Z²+Z+C)/(Z-C)

106 -- F(Z) = exp(Z²+C)

107 -- F(Z) = Z²*exp(Z²)+C

108 -- F(Z) = exp(Z²)/(Z+C)

109 -- F(Z) = (Z+exp(Z))²+C

110 -- F(Z) = (Z²+C)²-exp(Z)+C

111 -- F(Z) = (1+iC)sin(Z)

112 -- F(Z) = (1+iC)cos(Z)

113 -- F(Z) = Z*tan(log Z)+C

114 -- F(Z) = sqrt(Z⁴+1)+C

115 -- F(Z) = sqrt(Z⁴+C)

116 -- F(Z) = C^Z

117 -- F(Z) = C*arctan(Z)

118 -- F(Z) = (ZlogZ)/exp(C)

119 -- F(Z) = exp(Z)/logZ+C

120 -- F(Z) = sqrt(Z³+C)

121 -- F(Z) = sqrt(Z³+1)+C

122 -- F(Z) = cubrt(Z⁶+1)+C

123 -- F(Z) = (Z+exp(Z)+log Z)²+C

124 -- F(Z) = (Z²+C+1)² / (2Z+C+2)²

125 -- F(Z) = Z¹⁰ + C

126 -- F(Z) = Z¹¹ + C

127 -- F(Z) = Z¹² + C

128 -- F(Z) = Z¹² - Z¹¹ - Z¹⁰ + C

129 -- F(Z) = Z¹³ + C

130 -- F(Z) = Z¹⁴ + C

131 -- F(Z) = Z¹⁵ + C

132 -- F(Z) = Z¹⁶ + C

133 -- F(Z) = Z¹⁷ + C

134 -- F(Z) = Z¹⁸ + C

135 -- F(Z) = Z¹⁹ + C

136 -- F(Z) = Z²⁰ + C

137 -- F(Z) = Z²¹ + C

138 -- F(Z) = Z²² + C

139 -- F(Z) = Z²³ + C

140 -- F(Z) = Z²⁴ + C

141 -- F(Z) = Z²⁵ + C

142 -- F(Z) = Z²⁶ + C

143 -- F(Z) = Z²⁷ + C

144 -- F(Z) = Z²⁸ + C

145 -- F(Z) = Z²⁹ + C

146 -- F(Z) = Z³⁰ + C

147 -- X=X²+Y+A+X²/Y ;Y=Y²+X+B+Y²/X

148 -- X=X³+Y²-X+A ;Y=Y³-X²+Y+B

149 -- X=X²+2XY-Y+A ;Y=Y²-2XY+X+B

150 -- X=X³+AX²+BY ;Y=Y³+BY²+AX

151 -- X=2X²-3ABY+A ;Y=3Y²+2ABX-B

152 -- X=X⁴logX+Y²sinY+A; Y=Y⁴logY+X²cosX+B

153 -- X=sqr(log(X²))+YsinX+A; Y=sqr(log(Y²))-XcosY+B

154 -- X=.5(X²-Y²)+.5(X+Y)+A; Y=.5(Y²-X²)-.5(X+Y)+B

155 -- X=sqr(X³)+sqr(Y³)+A; Y=sqr(Y³)-sqr(X³)+B

156 -- X=Y/sqrX+X/sqrY+A; Y=XsqrY+YsqrX+B

157 -- F(Z) = Z³⁰ - 30Z²⁹ - 870Z²⁸ + C

158 -- F(Z) = Z²⁷ - 27Z²⁶ - 702Z²⁵ + C

159 -- F(Z) = Z²⁴ - 24Z²³ - 552Z²² + C

160 -- F(Z) = Z²¹ - 21Z²⁰ - 420Z¹⁹ + C

161 -- F(Z) = Z¹⁸ - 18Z¹⁷ - 306Z¹⁶ + C

162 -- F(Z) = Z¹⁵ - 15Z¹⁴ - 210Z¹³ + C

163 -- F(Z) = Z³⁰ - 30Z²⁹ - 870Z²⁸ + Z²⁷ - 27Z²⁶ - 702Z²⁵ + C

164 -- F(Z) = Z²⁷ - 27Z²⁶ - 702Z²⁵ + Z²⁴ - 24Z²³ - 552Z²² + C

165 -- F(Z) = Z²⁴ - 24Z²³ - 552Z²² + Z²¹ - 21Z²⁰ - 420Z¹⁹ + C

166 -- F(Z) = Z²¹ - 21Z²⁰ - 420Z¹⁹ + Z¹⁸ - 18Z¹⁷ - 306Z¹⁶ + C

167 -- F(Z) = Z¹⁸ - 18Z¹⁷ - 306Z¹⁶ + Z¹⁵ - 15Z¹⁴ - 210Z¹³ + C

168 -- F(Z) = Z³⁰ - 30Z²⁹ - 870Z²⁸ + Z²⁷ - 27Z²⁶ - 702Z²⁵ + Z²⁴ - 24Z²³ -
552Z²² + C

169 -- F(Z) = Z²⁷ - 27Z²⁶ - 702Z²⁵ + Z²⁴ - 24Z²³ - 552Z²² + Z²¹ - 21Z²⁰ -
420Z¹⁹ + C

170 -- F(Z) = Z²⁴ - 24Z²³ - 552Z²² + Z²¹ - 21Z²⁰ - 420Z¹⁹ + Z¹⁸ - 18Z¹⁷ -
306Z¹⁶ + C

171 -- F(Z) = Z²¹ - 21Z²⁰ - 420Z¹⁹ + Z¹⁸ - 18Z¹⁷ - 306Z¹⁶ + Z¹⁵ - 15Z¹⁴ -
210Z¹³ + C

172 -- F(Z) = Z³⁰ - Z²⁹ + Z²⁸ - Z²⁷ + Z²⁶ - Z²⁵ + C

173 -- F(Z) = Z²⁴ - Z²³ + Z²² - Z²¹ + Z²⁰ - Z¹⁹ + C

174 -- F(Z) = Z¹⁸ - Z¹⁷ + Z¹⁶ - Z¹⁵ + Z¹⁴ - Z¹³ + C

175 -- F(Z) = Z¹⁵sinX - Z¹⁴cosY - Z¹³tanX + C

176 -- F(Z) = Z¹²cosX - Z¹¹sinY - Z¹⁰tanY + C

177 -- F(Z) = Z¹⁵sinA - Z¹⁴cosB - Z¹³tanX - Z¹²tanY + C

178 -- F(Z) = Z¹²cosA - Z¹¹sinB - Z¹⁰tanY - Z⁹tanX + C

179 -- F(Z) = Z³⁰sinX - 30Z²⁹cosY + C

180 -- F(Z) = Z²⁸cosX - 28Z²⁷sinY + C

181 -- F(Z) = (Z³+3Z(C-1)+(C-1)(C-2))²

182 -- F(Z) = (3Z²+3Z(C-2)+C²-3C+3)²

183 -- F(Z) = (Z³+3Z(C-1)+(C-1)(C-2))² / (3Z²+3Z(C-2)+C²-3C+3)²

184 -- F(Z) = Z ^ pi + C

185 -- F(Z) = pi ^ Z + C

186 -- F(Z) = Z⁴ + C

187 -- F(Z) = Z ^ pi + pi ^ C

188 -- F(Z) = C * Z ^ pi

189 -- F(Z) = Z ^ pi - Z³ + C

190 -- F(Z) = Z ^ pi - Z² + C

191 -- F(Z) = Z².5 + C

192 -- F(Z) = (5Z⁶ + C)/6Z⁵

193 -- F(Z) = Z ^ e + C

194 -- F(Z) = Z ^ (C * e)

195 -- F(Z) = (Z ^ e) ^ C

196 -- F(Z) = C * Z ^ e

197 -- F(Z) = Z ^ (pi * e)

198 -- F(Z) = Z * (C ^ e)

199 -- F(Z) = cbrt(Z⁷ + 1) + C

200 -- F(Z) = Z⁴.669 + C

201 -- F(Z) = (Z⁸ + 1) ^ 1/4 + C

202 -- F(Z) = (Z⁹ + 1) ^ 1/4 + C

203 -- F(Z) = ((Z² * (X - (Y)²))/(1 - Z)) + C

204 -- F(Z) = (Z¹⁰ + C) ^ 1/4

205 -- F(Z) = (Z¹⁰ + 1) ^ 1/4 + C

206 -- F(Z) = (Z¹¹ + C) ^ 1/4

207 -- F(Z) = (Z¹¹ + 1) ^ 1/4 + C

208 -- F(Z) = (Z¹² + C) ^ 1/4

209 -- F(Z) = (Z¹² + 1) ^ 1/4 + C

210 -- F(Z) = YZ²sinX - XZcosY + C

211 -- F(Z) = XZ³cosY + YZ²sinX + C

212 -- F(Z) = Z⁴ - Z²cosX + YsinY + C

213 -- F(Z) = XYZ² + C

214 -- F(Z) = Z² + X²*Y² + C

215 -- F(Z) = Z³ + X²sinY + Y²cosX + C

216 -- F(Z) = (Z¹³ + C) ^ 1/6

217 -- F(Z) = (Z⁵ + C) ^ 1/3

218 -- F(Z) = (Z⁴ + C) ^ 1/sin X

219 -- F(Z) = Z² + iZ² + C

220 -- F(Z) = Z³ + iZ³ + C

221 -- F(Z) = Z⁴ + iZ² + C

222 -- F(Z) = (Z⁴ / Z + 1) + C

223 -- F(Z) = (Z⁶ / Z + 1) + C

224 -- F(Z) = (Z⁴ / Z + i) + C

225 -- F(Z) = (Z⁶ / Z + i) + C

226 -- F(Z) = (Z² / (logZ)²) + C

227 -- F(Z) = (Z² / (log(Z²)) + C

228 -- F(Z) = (Z³ / (logZ)³) + C

229 -- F(Z) = (Z³ / (log(Z³)) + C

230 -- F(Z) = (Z⁴ / (logZ)⁴) + C

231 -- F(Z) = (Z⁴ / (log(Z⁴)) + C

232 -- F(Z) = Z² + Z / log Z + C

233 -- F(Z) = Z² + log Z / Z + C

234 -- F(Z) = Z⁶ + Z⁴ + Z² + C

235 -- F(Z) = Z⁶ - Z⁴ - Z² + C

236 -- F(Z) = Z ^ (1/Z) + C

237 -- F(Z) = Z² + sin(Z) / Z + C

238 -- F(Z) = Z² + Z / sin(Z) + C

239 -- F(Z) = Z ^ iZ + C

240 -- F(Z) = Z² * exp(X) + C

241 -- F(Z) = Z² * exp(X²) + C

242 -- F(Z) = Z³ * exp(X) + Z² * exp(Y) + C

243 -- F(Z) = exp(Z ^ Z) + C

244 -- F(Z) = (Z³) / (Z + 1) + C

245 -- F(Z) = Z² / C

246 -- F(Z) = (Z⁴ + 1) / (Z + C)

247 -- F(Z) = (Z⁴ + C) / (Z² + 1)

248 -- F(Z) = (Z⁴ + C) / (1 - Z²)

249 -- F(Z) = Z² * exp(Z) / (Z + C)

250 -- F(Z) = Z² - exp(Z) + sin(Z) + C

251 -- F(Z) = (Z⁴) / (Z² + C)

252 -- F(Z) = Z² + sqrt(Z² + C)

253 -- F(X) = X² - Y² + XsinY + A; F(Y) = Y² - B

254 -- F(X) = X² + atan(Y/X) + A; F(Y) = Y² - A

255 -- F(X) = 1 - X - Y² + A; F(Y) = 1 - Y + X² + B

256 -- F(X) = exp(sqrt(X)) - exp(sqrt(Y)) + A; F(Y) = exp(XlogY) + B

257 -- F(Z) = C² * log(Z²)

258 -- F(Z) = Z² log(C)

259 -- F(Z) = Z² log(C) + C

260 -- F(Z) = Z² log(Z + C)

261 -- F(Z) = Z ^ -2 + C

262 -- F(Z) = ((X² + Y² + A) / (X² - Y²)) + i[((X² - Y² - B) / (X² + Y²))]

263 -- F(Z) = (X³ - iY + C) / (X + Y + 1)

264 -- F(Z) = [(X² + A²) / Y] + i[(Y² + B²) / X]

265 -- F(Z) = [(X³ + X² + X + A) / (Y³ - Y² - Y - 1)] + i[(Y³ + Y² + Y + B) /
(X³ - X² - X - 1)]

266 -- F(Z) = [(X⁴ - Y²) / (X + Y + A)] + i[(X² + Y⁴) / (X - Y - B)]

267 -- F(Z) = C³ / Z²

268 -- F(Z) = [Z^(1/2) / Z^(1/3)] + C

269 -- F(Z) = (Z² + C) / (1 - C)

270 -- F(Z) = (exp(Z⁴)/ Z⁴) + C

271 -- F(Z) = (Z⁶ + 1) ^ (1/5) + C

272 -- F(Z) = Z² + CZ + C * sin Y - Z * cos X + C

273 -- F(Z) = Z⁶ - Z⁵ - Z⁴ - Z³ - Z² - Z + C

274 -- F(Z) = Z² * (sin C / C)

275 -- F(Z) = exp(- Z² / 2) + C

276 -- F(Z) = (Z³ + 3 * Z - 1) / (2 - Z)

277 -- F(Z) = Z³ * sin C + Z² * cos C + XY + C

278 -- F(Z) = (Z² + 1)² / (Z + C)²

279 -- F(Z) = (Z² + C + 1)² / (Z - C - 1)²

280 -- F(Z) = Z⁴ * sin Y + Z² * cos X + XY + C

281 -- F(Z) = Z * cos (XY) + C

282 -- F(Z) = Z² * cos (X² + Y²) + C

283 -- F(Z) = Z ^ (2 + log C)

284 -- F(Z) = Z ^ (9/7) + C

285 -- F(Z) = Z⁵ * (1 - Z - (Z + C)²) + C

286 -- F(Z) = Z⁶ + Z⁵ + C

287 -- F(Z) = Z⁶ + Z⁴ + C

288 -- F(Z) = Z⁶ + Z³ + C

289 -- F(Z) = Z⁶ + Z² + C

290 -- F(Z) = Z⁶ + Z + C

291 -- F(Z) = Z² + cos(Z) + C

292 -- F(Z) = Z² + cos 2Z + C

293 -- F(Z) = Z² + cos 3Z + C

294 -- F(Z) = Z² + cos 4Z + C

295 -- F(Z) = Z² + cos 5Z + C

296 -- F(Z) = (Z⁷ + C) / Z⁵

297 -- F(Z) = (Z⁷ + C) / Z⁴

298 -- F(Z) = (Z⁷ + C) / Z³

299 -- F(Z) = (Z⁷ + C) / Z²

300 -- F(Z) = (Z⁷ + C) / Z

301 -- F(Z) = Z³ - Z² - Z + C

302 -- F(Z) = Z⁴ - Z³ - Z² + C

303 -- F(Z) = Z⁵ - Z⁴ - Z³ + C

304 -- F(Z) = Z⁶ - Z⁵ - Z⁴ + C

305 -- F(Z) = Z⁷ - Z⁶ - Z⁵ + C

306 -- F(Z) = Z² * (cos(Z))² + C

307 -- F(Z) = Z² * (cos(XY))² + C

308 -- F(Z) = Z⁴ * (sin(Z))² + C

309 -- F(Z) = Z³ * (sin(XY))² + C

310 -- F(Z) = Z³ * (cos(Z)*sin(Z)) + C

311 -- F(Z) = (Z² / sin(Z)) + C

312 -- F(Z) = (Z⁴ / cos(Z)) + C

313 -- F(Z) = (Z⁶ + C) / (sin(Z) * cos(Z))

314 -- F(Z) = (Z³ + Z² + Z + C) / (Z + cos(Z)

315 -- F(Z) = (Z² * log Z + Z + C) / (sin(Z))²

316 -- F(Z) = Z⁴ + (cos X)² + (sin Y)² + C

317 -- F(Z) = Z³ + cos X * sin Y + C

318 -- F(Z) = Z⁴ + Z + cos C

319 -- F(Z) = Z² + Z + tan C

320 -- F(Z) = Z³ + Z² + exp(1 + sin X) + C

321 -- F(Z) = sqrt(Z⁴ + cos(theta) + C); theta = arctan (Y / X)

322 -- F(Z) = sqrt(Z⁵ + Z³ + Z + C)

323 -- F(Z) = sqrt(Z⁴ + Z³ + Z² + Z + C)

324 -- F(Z) = sqrt(Z⁶ - Z³ + C)

325 -- F(Z) = sqrt(log (Z²) + Z² * log Z + C)

326 -- F(Z) = cos((Z² + C) / XY)

327 -- F(Z) = cos((Z³ + C) / XY)

328 -- F(Z) = cos((Z⁴ + C) / XY)

329 -- F(Z) = ((Z⁴ + C) / XY) + cos((Z³ + C) / XY)

330 -- F(Z) = cos((Z⁴ + C) / XY) + cos((Z³ + C) / XY) + cos((Z² + C) / XY)

331 -- F(Z) = Z³/2 + Z⁴/3 + C

332 -- F(Z) = Z⁴/3 + Z⁵/4 + C

333 -- F(Z) = Z⁵/4 + Z⁶/5 + C

334 -- F(Z) = Z⁵/2 + Z⁷/3 + C

335 -- F(Z) = Z ^ (pi/e)² + C

336 -- F(Z) = Y * sin X * cos Y * exp(-X) + C

337 -- F(Z) = Z² * cos X * cos Y * exp(-Y) + C

338 -- F(Z) = XYZ * sin X * sin Y * exp(Z) + C

339 -- F(Z) = Z³ + X² * Y² * cos X * sin Y + C

340 -- F(Z) = Z² + X² * sin Y + Y² * cos X + C

341 -- F(Z) = 1 / Z + 1 / Z² + C

342 -- F(Z) = Z² / Z' + Z³ / Z'² + C

343 -- F(Z) = Z³ / C' + Z² + C

344 -- F(Z) = Z² + Z'² + C

345 -- F(Z) = Z³ + Z² * Z' + Z * Z'² + Z'³ + C

346 -- F(Z) = Z⁴ - Z³ * Z' + Z² - Z' + C

347 -- F(Z) = Z⁵ - C * Z³ - C' * Z² + Z' + C

348 -- F(Z) = Z⁴ * Z'² - Z³ * Z' + C

349 -- F(Z) = Z⁶ + Z'⁵ + Z⁴ + Z'³ + Z² + Z' + C

350 -- F(Z) = Z⁴ + Z² / Z' + Z'³ / Z² + C

351 -- F(Z) = arcsin(log(Z)) + C

352 -- F(Z) = arctan(log(Z)) + C

353 -- F(Z) = (arcsin(log(Z)))² + C

354 -- F(Z) = e ^ (1 + cos(log(Z))) + C

355 -- F(Z) = e ^ (2 - e ^ cos(Z)) + C

356 -- F(Z) = XY * Z² - X² * YZ + X * Y² * Z³ + C

357 -- F(Z) = X³ * Y⁴ + X² * Z⁵ + C

358 -- F(Z) = XY²Z³ - X³Y²Z + X²Y²Z² + C

359 -- F(Z) = Z⁴ - X² * cos(Y) + Y * sin(X) + C

360 -- F(Z) = Z³ - Y² * cos(XY) - X² * sin(X) - Y * cos(Y) + C

361 -- F(Z) = (Z³ + C) / (Z³ - C)

362 -- F(Z) = (Z³ + C² + 1) / (Z³ - C² - 1)

363 -- F(Z) = (Z³ + Z + C) / (Z³ - Z - 1)

364 -- F(Z) = (Z² - Z³ + 1) / (Z⁴ + C)

365 -- F(Z) = (Z⁴ + C) / (4Z³ + 1)

366 -- F(Z) = (Z ^ C) / (Z + 1)

367 -- F(Z) = (Z ^ (1 + C)) / (1 + C)

368 -- F(Z) = (2 ^ Z) / C

369 -- F(Z) = 2 ^ Z + C

370 -- F(Z) = 2 ^ Z + (2 ^ Z) / C + C

371 -- F(Z) = XYZ² - X²YZ + C

372 -- F(Z) = X⁴ * Y³ * Z² + C

373 -- F(Z) = X³*Y³*Z³ - X²*Y²*Z² + XYZ + C

374 -- F(Z) = XY²Z + X²YZ⁴ + C

375 -- F(Z) = Z²*sqrt(XY) + XY²Z⁴*sqrt(XY) + C

376 -- F(Z) = Z ^ (2XY) + C

377 -- F(Z) = X ^ (2YZ) + C

378 -- F(Z) = Y ^ (Z²) + X + C

379 -- F(Z) = X ^ (2YZ) + Z ^ (2XY) + C

380 -- F(Z) = (XY) ^ (Z - C)

381 -- F(Z) = Z²C + C

382 -- F(Z) = Z² + C²Z + C

383 -- F(Z) = X^Y + Z^X + Y^Z + C

384 -- F(Z) = Z² + A ^ X + B ^ Y + C

385 -- F(Z) = Z³ + X ^ (AB) + Y ^ C

386 -- F(Z) = Z⁹ - Z⁸ - Z⁷ + C

387 -- F(Z) = Z⁹ - 9Z⁸ - 8Z⁷ + C

388 -- F(Z) = Z⁹ - 9Z⁸ - 8Z⁷ - 7Z⁶ - 6Z⁵ - 5Z⁴ + C

389 -- F(Z) = Z⁹ - 9Z⁸ - 8Z⁷ - 7Z⁶ - 6Z⁵ - 5Z⁴ - 4Z³ - 3Z² - 2Z +C

390 -- F(Z) = Z⁹ + C⁹

391 -- F(Z) = Z³ + Z² + CsinX + C

392 -- F(Z) = Z⁴ + X² - Y² - C²*cos(Z) + C + A

393 -- F(Z) = Z⁵ + Im(Z⁴ + Z³ + Z²) + CZRe(Z² + C) + C

394 -- F(Z) = Z³ + Z²*cosY + ZsinX + C

395 -- F(Z) = Z⁴ + (Z² / sinY) + (CZ³ / cosX) + C

396 -- F(Z) = (Z + log Z)⁴ + C

397 -- F(Z) = Z + (log Z)⁴ + C

398 -- F(Z) = Z² + (log Z)³ + C

399 -- F(Z) = Z³ + (log Z)² + C

400 -- F(Z) = (log Z)² + C² + C

401 -- F(Z) = Z² + C + A

402 -- F(Z) = Z² + C + iB

403 -- F(Z) = Z² + C + X

404 -- F(Z) = Z² + C + iY

405 -- F(Z) = Z² + C + iXY

406 -- F(Z) = X³ + X²Y - XY² + Y³ + C

407 -- F(Z) = X⁵ + iX⁴ -iX³Y + iX²Y² - iXY³ + iY⁴ + C

408 -- F(Z) = Y³ - Y² - Y - 1 - A + iX³ + iX² + iX + i + iB

409 -- F(Z) = Y⁴ + Y² + A - iX⁴ - iX² - iB

410 -- F(Z) = X² + X + 1 + A + iY² - iY - i - iB

411 -- F(Z) = arcsin(Z) + C (3rd appr)

412 -- F(Z) = 1 - Z/X - Z²/Y + C

413 -- F(Z) = arctan(Z) + C (5th appr)

414 -- F(Z) = X³/Y² + Y⁴/X³ + A + i(Y²/X) - i(X³/Y) + iB

415 -- F(Z) = Z⁴/(X+Y) + Z³/(X-Y) + C

416 -- F(Z) = Z^(2-X) + C

417 -- F(Z) = Z^(2-X-Y) + C

418 -- F(Z) = Z^(3+C)

419 -- F(Z) = Z^(2X² - 3Y²) + C

420 -- F(Z) = (X+Y)²Z + C

421 -- F(Z) = Z² + sin(Z)*cos(Z) + C

422 -- F(Z) = Z² + sec(Z)*tan(Z) + C

423 -- F(Z) = Z² + sin(Z)*tan(Z) + C

424 -- F(Z) = Z² + cot(Z)*arcsin(Z) + C

425 -- F(Z) = Z² + tan(Z)*arccos(Z) + C

426 -- F(Z) = Z^(2-Z) + C

427 -- F(Z) = Z^(3-Z) + C

428 -- F(Z) = Z^(4-Z) + C

429 -- F(Z) = Z^(5-Z) + C

430 -- F(Z) = Z^(6-Z) + C

431 -- F(Z) = Z^(2-C) + C

432 -- F(Z) = Z^(3-C) + C

433 -- F(Z) = Z^(4-C) + C

434 -- F(Z) = Z^(5-C) + C

435 -- F(Z) = Z^(6-C) + C

436 -- F(Z) = Z^Z / Z^C

437 -- F(Z) = C^Z / Z^Z

438 -- F(Z) = (1-C)²Z

439 -- F(Z) = (Z+C)^Z

440 -- F(Z) = (Z² + C²)²Z

441 -- F(Z) = Z^CZ

442 -- F(Z) = Z^(C²) + C

443 -- F(Z) = C^(2^Z) + C

444 -- F(Z) = Z^(tan(Z) + C

445 -- F(Z) = Z^(sin(Z)cos(Z)) + C

446 -- F(Z) = 2CZ / (Z + C)

447 -- F(Z) = 2CZ / sqrt(Z + C)

448 -- F(Z) = 2 * Z² * C² / (Z + C)

449 -- F(Z) = 2CZ³ / (Z + C)

450 -- F(Z) = sqrt(2CZ) / (Z + C)

451 -- F(Z) = Z ^ (Z/C)

452 -- F(Z) = Z² + Z ^ (Z/C)

453 -- F(Z) = Z ^ (Z/C) + Z + C

454 -- F(Z) = Z ^ (Z/C) Z² + C

455 -- F(Z) = Z ^ (Z² / C)

456 -- F(Z) = Z ^ (C/Z)

457 -- F(Z) = Z ^ (C/Z) + Z

458 -- F(Z) = Z ^ (C/Z) + Z²

459 -- F(Z) = Z ^ (C/Z) + C

460 -- F(Z) = Z ^ (C² / Z)

461 -- F(Z) = Z ^ log(Z ^ Z/C)

462 -- F(Z) = Z ^ log(Z ^ C/Z)

463 -- F(Z) = Z ^ Z/C + Z ^ C/Z

464 -- F(Z) = sqrt(X² + Y²) + iarctan(Y/X) + C

465 -- F(Z) = Z² + sqrt(X² + Y²) + iarctan(Y/X) + C

466 -- F(Z) = Z³ + sqrt(X² + Y²) + iarctan(Y/X) + C

467 -- F(Z) = Z⁴ + sqrt(X² + Y²) + iarctan(Y/X) + C

468 -- F(Z) = Z² + sqrt(A² + B²) + iarctan(B/A)

469 -- F(Z) = Z³ + sqrt(X³ + Y³) + C

470 -- F(Z) = Z⁴ + sqrt(X⁴ + Y⁴) + C

471 -- F(Z) = Z⁵ + sqrt(X⁵ + Y⁵) + C

472 -- F(Z) = Z⁶ + sqrt(X⁶ + Y⁶) + C

473 -- F(Z) = Z⁷ + sqrt(X⁷ + Y⁷) + C

474 -- F(Z) = Z⁸ + sqrt(X⁸ + Y⁸) + C

475 -- F(Z) = Z⁹ + sqrt(X⁹ + Y⁹) + C

476 -- F(Z) = sqrt(X² + Y²) + isqrt(X³ + Y³)

477 -- F(Z) = sqrt(X³ + Y³) + isqrt(X⁴ + Y⁴)

478 -- F(Z) = sqrt(X⁴ + Y⁴) + isqrt(X⁵ + Y⁵)

479 -- F(Z) = sqrt(X⁵ + Y⁵) + isqrt(X⁶ + Y⁶)

480 -- F(Z) = sqrt(X⁶ + Y⁶) + isqrt(X⁷ + Y⁷)

481 -- F(Z) = Z² + exp(cot(Z))*cot(Z)

482 -- F(Z) = Z² + exp(tan(Z))*tan(Z)

483 -- F(Z) = Z² + exp(cos(Z))*cos(Z)

484 -- F(Z) = Z² + exp(sin(Z))*sin(Z)

485 -- F(Z) = Z² + (exp(cot(Z))/ Z) + C

486 -- F(Z) = Z * det|X A Y B| + i * det|A Y B X| + C

487 -- F(Z) = Z² + det|X A Y B| + C

488 -- F(Z) = Z² * C² * det|X A Y B| + C

489 -- F(Z) = Z³ * C³ * det|X A Y B| - C

490 -- F(Z) = 2XY - i(X² - Y³) + C

491 -- F(Z) = 3*X³*Y² - iZ² + C

492 -- F(Z) = ZC³ - Z²*C² - CZ³ + C\n");

493 -- F(Z) = X²*Y*Z² - Y²*Z*sin(X) + X²*cos(Y) + C

494 -- F(Z) = Y³*Z³ - ZX² - C² * sin(Y) + C

495 -- F(Z) = X²*Y²*Z²*C² + CXYZ + iZ³

496 -- F(Z) = X³*Y³*Z³ + iCXZ²

497 -- F(Z) = X²*Y⁸*Z⁵ + iXYZC⁴

498 -- F(Z) = X²*Y³*Z⁴ + XY²*Z³ + Z² + C

499 -- F(Z) = XYZ²*cos(X) + X² - Y² + BCZ + C

500 -- F(Z) = Z² + ABXY + C

The next fifty-two equations are exhibited
in the 2005 "M" line of fractal imagery.

501 -- F(Z) = Z^C + SIN C

502 -- F(Z) = (sqrt Z + C) / C

503 -- F(Z) = (SIN(Z+1))^Z * COS(1/Z) + C

504 -- F(Z) = SIN(Z * COS Z + C) + C

505 -- F(Z) = COS(Z² / C) + SIN(C / Z²) + C

506 -- F(Z) = Z^C + C^Z + C^(Z²) + Z^(C²)

507 -- F(Z) = ((Z + SIN(Z) + C)² + C) / Z

508 -- F(Z) = SIN(COS(Z² + C) + Z + C

509 -- F(Z) = SIN(Z²) * log(C²) * (Z * C^(sqrt(Z)) + C

510 -- F(Z) = Z² + Z * C^(sqrt(Z)) + C

511 -- F(Z) = SIN(Z² / C) + COS(Z / C) + Z² + C

512 -- F(Z) = ((Z⁴ + C) / (Z² - C)) + Z² + C

513 -- F(Z) = ((Z² + C)² + Z - C³) / 2(Z² + C)

514 -- F(Z) = e^(Z²) + e²Z - Z² - 1 + C

515 -- F(Z) = (2e²Z / Z³) + C

516 -- F(Z) = 3Z² * 3^(Z³) - 3^Z + C

517 -- F(Z) = (1 + log(Z))³ + C

518 -- F(Z) = (Z + 1/Z)².5 + C

519 -- F(Z) = (Z^(Z - 1) + 1)² + C

520 -- F(Z) = (1 / log(Z + C))

521 -- F(Z) = C * (Z + 1/Z) + Z^(-.5) + C

522 -- F(Z) = Z² + Z^1.75 + Z^1.5 + Z^1.25 + Z + C

523 -- F(Z) = ((Z⁴ + Z² + C)² / (Z⁵ + Z³ + Z + C))

524 -- F(Z) = (1 / SINH(1 / Z²)) + C

525 -- F(Z) = (Z ^ C + Z) / C

526 -- F(Z) = (Z + C^Z) / C

527 -- F(Z) = (Z^C + C) / Z

528 -- F(Z) = (C^Z + C) / Z

529 -- F(Z) = Z^1.75 + C

530 -- F(Z) = (Z².5 / log(Z)) + C

531 -- F(Z) = Z² * log(Z) - C*Z + Z + C

532 -- F(Z) = sqrt(Z⁶ + Z + C) + C

533 -- F(Z) = (C * Z²)^Y + C

534 -- F(Z) = sqrt(Z⁴ + Z³) + Z + C

535 -- F(Z) = (((Z² + X - 1)²) / (2Z + X + 1)²) + C

536 -- F(Z) = Z² + X + Y - X² * Y² + C

537 -- F(Z) = Z^(Z² + C) - Z + C

538 -- F(Z) = (Z + TAN(Z) + TAN(1/Z))² + C

539 -- F(Z) = Z^(C - 1) * (1 - Z - Z²) + C

540 -- F(Z) = log(1 / (COS(Z² + C)))

541 -- F(Z) = Z³ + (TAN(Z) + C * Z)²

542 -- F(Z) = Z² * X - Z * Y + C

543 -- F(Z) = Z² * CSC(Z²) + C

544 -- F(Z) = (Z + log(Z))³ + C

545 -- F(Z) = Z^(log(Z²)) - Z + C

546 -- F(Z) = (2Z⁴ - Z + C) / (Z + C)

547 -- F(Z) = Z⁵C - Z³C + Z^C + C

548 -- F(Z) = Z² + ((Z³) / (TAN(Z)²))) + C

549 -- F(Z) = C^(Z² - Z + C)

550 -- F(Z) = Z⁷ + ((Z⁵) / (5 - Z)) + ((Z³) / (3 - Z)) + Z / C

551 -- F(Z) = (TAN(C * Z))² + C

552 -- F(Z) = Z³ + (1 + log(Z))² + C

The next group of 55 equations are exhibited
in the 2006 "D" line of fractal imagery.

553 -- F(Z) = Z ^ (2 / SIN Z) + C

554 -- F(Z) = Z ^ (2 / TAN Z) + C

555 -- F(Z) = Z ^ (3 / COS Z) + C

556 -- F(Z) = Z ^ (3 / TAN Z) + C

557 -- F(Z) = Z ^ (2 / (1 + log Z)) + C

558 -- F(Z) = Z ^ (3 / (1 + log Z)) + C

559 -- F(Z) = Z ^ (2 / (ATAN Z) + C

560 -- F(Z) = Z ^ (3 / (ATAN Z) + C

561 -- F(Z) = (1 + Z ^ (2/Z)) ^ Z + C

562 -- F(Z) = (1 + Z ^ (2/(1-Z²))) + C

563 -- F(Z) = (1 + Z ^ (2/(1-Z)))² + C

564 -- F(Z) = (1 + Z ^ (2/(1-Z²)))² + C

565 -- F(Z) = (1 + Z ^ (2/(1-Z))) ^ Z + C

566 -- F(Z) = (1 + Z ^ (4/Z²)) + C

567 -- F(Z) = (Z² - z ^ (4/Z)) + C

568 -- F(Z) = (Z + ATAN(1 / Z))² + C

569 -- F(Z) = (Z + ATAN(1 / C))² + C

570 -- F(Z) = (1 + Z * ATAN(Z))² + C

571 -- F(Z) = (Z + C * ATAN(sqrt(Z)))² + C

572 -- F(Z) = (Z + ATAN(1/Z))³ + C

573 -- F(Z) = (Z + (1 / (ATAN(1/Z)))² + C

574 -- F(Z) = (Z + (C / (ATAN(1/Z)))²

575 -- F(Z) = Z⁵ + (1 + ATAN(Z))² + C

576 -- F(Z) = Z⁴ + (1 - TAN(1/Z))² + C

577 -- F(Z) = Z³ + (C + 1/Z)² + C

578 -- F(Z) = Z⁴ - 3X³ - 2Y² - Z + C

579 -- F(Z) = (Z⁶ / (6Z⁵ + C) + C

580 -- F(Z) = ((Z⁶ + C )/ (5Z⁴)) + C

581 -- F(Z) = ((Z⁵ + C )/ (4Z³)) + C

582 -- F(Z) = ((Z⁴ + Z³) / (3Z² + C)) + C

583 -- F(Z) = C / (Z² * log Z)

584 -- F(Z) = (1 / (Z² * log Z)) + C

585 -- F(Z) = 1/Z⁴ - 1/Z³ + 1/Z² - 1/Z + C

586 -- F(Z) = X² * SIN Z + Y² * COS Z + Z² + C

587 -- F(Z) = X² * Y² - Z² + Z + C

588 -- F(Z) = Z² + XYC² + C

589 -- F(Z) = Z² + ATAN(Z²) + C

590 -- F(Z) = X²*Y - X*Y² + Z + C

591 -- F(Z) = X²*Y²*Z² + ATAN Z + C

592 -- F(Z) = Z² + (ATAN (XYZ))² + C

593 -- F(Z) = (1 + log(1 + Z))² + C

594 -- F(Z) = (Z⁴ + C) / (ATAN Z)

595 -- F(Z) = (1 + (Z / ACOS Z))² + C

596 -- F(Z) = (1 + sqrt(Z² + ATAN Z))² + C

597 -- F(Z) = (Z² + sqrt(1 + (log Z)²))² + C

598 -- F(Z) = Z ^ (2 + ATAN Z + C)

599 -- F(Z) = C ^ (Z² + (1 /(1 + log Z))) + C

600 -- F(Z) = (1 + ATAN Z)² + (1 + ATAN 2Z)² + C

601 -- F(Z) = (1 + Z + ATAN 3Z)² + C

602 -- F(Z) = (Z + ((1 + ATAN 2Z)²)) + C

603 -- F(Z) = (1 + ACOS Z)² + C

604 -- F(Z) = (1 + XYZ)² + C

605 -- F(Z) = Z² - X²*Y*ACOS Z + C

606 -- F(Z) = Z³ + XY³ + X²*Z³ - YZ + C

607 -- F(Z) = Z⁴ - YZ³ + XZ² - ZC² + C

608 -- F(Z) = Z^(3/2) - (3/2)Z + Z^(1/2) + C

The next group of 71 equations are exhibited in the
brand new 2008 "W" line of fractal imagery.

609 -- F(Z) = (C / (1 - Z))² + C

610 -- F(Z) = ((Z² + 1) / ( 1 - Z))² + C

611 -- F(Z) = ((Z³ - XY² + YZ + 1) / (1 - X - Y)) + C

612 -- F(Z) = ((Z⁵ + CZ³ - C²*Z) / (1 + X² + Y² - Z)) + C

613 -- F(Z) = Z^(5/2)*X^(3/2)*Y^(1/2) + C

614 -- F(Z) = Z³ + (1 - XY)² + C

615 -- F(Z) = Z⁴ + (1 + X)² - (1 - Y)² + C

616 -- F(Z) = (Z⁷ + C) / (1 + X³ - Y³)

617 -- F(Z) = ((Z⁶ + X + Y³) / (1 - Z² + Y²)) + C

618 -- F(Z) = ((XZ⁴ - YZ³ + C) / (1 + XZ - YZ²)) + C

619 -- F(Z) = ((Z⁵ - Z³ + X² - Y) / (1 + CXY + Z²)) + C

620 -- F(Z) = Z^(5/2) - Z^(3/2) + C^(3/2) + C

621 -- F(Z) = (1 + C + Z) ^ (5/2) + C

622 -- F(Z) = Z ^ (1 - Z²) + C

623 -- F(Z) = Z ^ (Z - SIN Z) + C

624 -- F(Z) = Z ^ (1 + TAN Z) + C

625 -- F(Z) = Z ^ ((1 + log Z)²) + C

626 -- F(Z) = e ^ ((Z + C)²) + C

627 -- F(Z) = Z ^ (Z² / (1 - Z)) + C

628 -- F(Z) = Z ^ ((1 + TAN Z)²) + C

629 -- F(Z) = C ^ (Z + (1 + TAN Z)²) + C

630 -- F(Z) = Z ^ ((Z² + SIN(1/Z))²) + C

631 -- F(Z) = Z ^ (3 - Z) + Z ^ (1 + Z) + C

632 -- F(Z) = Z² COS X + Z + C

633 -- F(Z) = Z³ * (COS X)² + Z² * SIN Y + C

634 -- F(Z) = Z² * ATAN C + C

635 -- F(Z) = Z² * ACOS Z + C

636 -- F(Z) = Z² + (1 - COS Z)² + C

637 -- F(Z) = (e^Z - e^(-Z)) / C + C

638 -- F(Z) = Z² + SINH Z + C

639 -- F(Z) = (1 + Z + log(1 + Z²))² + C

640 -- F(Z) = (Z² / (Z + e^(1 - Z))) + c

641 -- F(Z) = ((Z³ + 2 log (1 + Z)) / e^Z) + C

642 -- F(Z) = (Z¹² - 12Z¹¹ - 11Z¹⁰ - 10Z⁹ + C) / (Z⁴ + Z² + 1)

643 -- F(Z) = (Z⁸ + Z⁶ + Z⁴ + Z² + 1) / (C³ + C² + C + 1)

644 -- F(Z) = Z⁷ - Z⁵ - Z³ + Z² + C

645 -- F(Z) = ((Z⁵ - Z⁴ + 1) / (Z³ - Z + 1)) + C

646 -- F(Z) = ((Z⁷ + Z³ + C) / (Z⁵ - C²)) + C

647 -- F(Z) = e^(1 + SIN Z) - e^(2 - COS Z) + Z^(2 - C) + C

648 -- F(Z) = sqrt(Z³ + Z²) + C

649 -- F(Z) = sqrt(Z⁴ + (1 + Z²)³) + C

650 -- F(Z) = sqrt(Z⁵ + Z³ + C) + C

651 -- F(Z) = sqrt(Z⁴ + (1 + e^Z)²) + C

652 -- F(Z) = sqrt(Z⁶ + (1 + COS Z)²) + C

653 -- F(Z) = sqrt(Z⁴ + ATAN(X² + Y² + Z²)) + C

654 -- F(Z) = sqrt(Z⁶ + Z⁴ + Z² + 1) + C

655 -- F(Z) = sqrt(Z⁴ + e^(Z + SIN Z)) + C

656 -- F(Z) = sqrt(Z³ + (1 + Z)^(5/2)) + C

657 -- F(Z) = CBRT(Z⁷ + Z⁵ * e^Z) + C

658 -- F(Z) = CBRT(e^(Z² + C)) + C

659 -- F(Z) = CBRT(Z⁸ - Z⁵ + 1) + C

660 -- F(Z) = CBRT(1 + ABS(ATAN(Z))⁵ + Z⁴) + C

661 -- F(Z) = CBRT(Z⁶ - e^(2 - Z) + 1) + C

662 -- F(Z) = CBRT(e^(Z² * log(ABS(1+Z))) + 1) + C

663 -- F(Z) = (Z⁹ - Z⁴ + 1) ^ (e^Z) + C

664 -- F(Z) = Z^(5/2) + (1 + SIN (Z/2))² + C

665 -- F(Z) = (1 + SIN(Z + COS Z))² + C

666 -- F(Z) = (Z ^ (2 / COS Z))² + C

667 -- F(Z) = e ^ (Z* (1 + COS Z)²) + C

668 -- F(Z) = (e²Z / (1 - Z)²) + C

669 -- F(Z) = log(1 + Z² + Z⁴) + C

670 -- F(Z) = Z - Z³/6 + Z⁵/120 - Z⁷/5040 + C

671 -- F(Z) = e ^ Z ^ (5/2) + C

672 -- F(Z) = (Z³ + ABS Z + 1) ^ Z + C

673 -- F(Z) = Z² / (COS Z * (1 + TAN Z)) + C

674 -- F(Z) = Z ^ (7/2) + (7/2) ^ Z + C

675 -- F(Z) = Z⁶ + Z ^ (Z + 3) + C

676 -- F(Z) = e^Z * SIN Z + e^(-Z) * ( 1 + ATAN Z) + C

677 -- F(Z) = (1 + Z*e^(-Z))² + C

678 -- F(Z) = (Z^C / (1 + C)) + C

679 -- F(Z) = (Z^Z / (1 - Z)) + Z + C

1001 -- F1(Z) = Z^(10-Z) + Z + C; F2(Z) = (1+SIN(Z))² + C

1002 -- F1(Z) = Z^(11-Z²) - Z + C; F2(Z) = (Z+TAN(Z))² + C

1003 -- F1(Z) = Z¹²(1+SIN(Z)) - Z² + C; F2(Z) = Z^(1-Z²) + C

1004 -- F1(Z) = Z^(2 + COS(Z)) + C; F2(Z) = Z^(12.5) + C

1005 -- F1(Z) = Z¹².5 + C; F2(Z) = Z².05 + C

1006 -- F1(Z) = 1 + SIN(Z¹²) + C; F2(Z) = Z².5 - Z + C

1007 -- F1(Z) = Z^sqrt(12) + C; F2(Z) = Z²*(1 + SIN(Z)) - Z + C

1008 -- F1(Z) = X*COS(C²*Z^sqrt(12)) + C; F2(Z) = ATAN(Z⁵) + Z² + C

1009 -- F1(Z) = 1 + SIN(Z² + Z⁶ - Z¹²) + C; F2(Z) = 1 + log(2/Z + Z + Z²) + C

1010 -- F1(Z) = (Z + COS(Z))⁶ - (Z - SIN(Z))⁴ + C; F2(Z) = IMAG(Z³) + Z² + 1 + C

1011 -- F1(Z) = (Z¹² - Z⁹ + Z⁶) / (Z⁴ + 1) + C; F2(Z) = 1 + log(1 + REAL(Z²) + COS(Z³)) + C

1012 -- F1(Z) = (Z¹² + Z⁸ + Z⁴ + 1) / (Z⁷ - 1) + C; F2(Z) = 1 + log(1 + REAL(Z²) + COS(Z³)) + C

1013 -- F1(Z) = (Z + COS(Z))⁷ - (Z - COS(Z))⁵ + C; F2(Z) = 1 + log(Z + COS(Z³)) + C

1014 -- F1(Z) = (Z + SIN(Z))⁷ - (SIN(X) - Y)⁵ + C; F2(Z) = Z² + REAL(Z² + 1 + COS(Z²)) + C

1015 -- F1(Z) = (Z² + SIN(Z))⁵ + (SIN(X - Y)³ + C; F2(Z) = Z² + C

1016 -- F1(Z) = (Z³ + SIN(Z))⁸ - (SIN(X - Y)⁶ + C; F2(Z) = Z^(2-Z) + C

1017 -- F1(Z) = (1 + TANH(Z))⁴ - (SIN(Z) - Y)² + C; F2(Z) = Z^(4-Z) + C

1018 -- F1(Z) = (Z² + TAN(Z))⁵ - (X + COS(1-Z))² + C; F2(Z) = Z² + C

1019 -- F1(Z) = (Z³ + SIN(1 - Z²))³ + (Z² + COS(1-Z))² + C; F2(Z) = C - COS(Z²) + A

1020 -- F1(Z) = Z⁴ + Z^C² + C; F2(Z) = ATAN(Z²) + COS(1 - Z²) + C

1021 -- F1(Z) = Z⁷ + Z^C³ + C; F2(Z) = REAL(Z²) + COS(1 - Z²) + C

1022 -- F1(Z) = Z⁵ + REAL(Z^(3-3COS(Z)) + C; F2(Z) = Z² + SIN(Z² + Z + 1) + C

1023 -- F1(Z) = Z⁵ + REAL(Z^(3-3COS(Z)) + C; F2(Z) = Z⁴ + ACOS(Z + SIN(Z² + Z + 1)) + C

1024 -- F1(Z) = Z^Z + Z⁷ + C; F2(Z) = Z³ + ATAN(Z² + SIN(Z² + Z + 2)) + C

1025 -- F1(Z) = Z⁵ + Z^(2/Z) + C; F2(Z) = Z³ + ACOS(Z²+ SIN(Z² +X + 2)) + C

1026 -- F1(Z) = (Z⁵ + Z^(2/Z) + C) / (Z³ + ACOS(Z²+ SIN(Z² +X + 2)) + C); F2(Z) = Z² + C

1027 -- F1(Z) = (Z¹⁵ + Z^(8/Z) + C) / (ACOS(Z³ + Z² +SIN(X)) + C; F2(Z) = Z² + C

1028 -- F1(Z) = Z¹¹ + Z^(4/Z) + C; F2(Z) = Z⁵ / (Z³ - Z + Y) + C

1029 -- F1(Z) = Z⁷ + Z^(5*COS(Z)) + C; F2(Z) = Z⁷ / (Z⁴ - Z² + X) + C

1030 -- F1(Z) = Z⁹ + Z^(7*TAN(Z)) + C; F2(Z) = Z⁶ / (Z⁴ + Z² + Y) + C

1031 -- F1(Z) = Z^(3SIN(1-Z) + Z⁶ + C; F2(Z) = (Z⁵COS(Z) / (Z³ - X + 1)) + C

1032 -- F1(Z) = Z⁵(1-COS(Z)) + Z⁸ + C; F2(Z) = (Z⁷SIN(Z) / (Z² + Y + 1)) + C

1033 -- F1(Z) = Z¹⁴(1-SIN(Z)) + Z¹¹.5 + C; F2(Z) = Z⁵log(Z) / (Z³ + Y - 1)) + C

1034 -- F1(Z) = Z¹¹.5SIN(1 - Z⁵) + Z⁵.5 + C; F2(Z) = Z⁷log(2-Z) / (Z⁴ + X - 1) + C

1035 -- F1(Z) = CZ⁷.5*COS(Z) + C; F2(Z) = (1 + sqrt(Z) + log(Z))⁹ + Z⁴ + C

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