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LegalizeAdulthood / iterated-dynamics

Iterated Dynamics is an open source fractal generator with support for many fractal types.
https://legalizeadulthood.github.io/iterated-dynamics/
GNU General Public License v3.0
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Add unique Tierazon fractal types #126

Open LegalizeAdulthood opened 3 weeks ago

LegalizeAdulthood commented 3 weeks ago

Tierazon has some fractal formulas that aren't in Id. Bring them over and document where existing fractal types cover Tierazon formulas, e.g. type=mandel.

LegalizeAdulthood commented 3 weeks ago

Compare against Appendix A. Mathematics of the Fractal Types

From the Tierazon resource script:

  1. [X] Mandel, z=z*z+c; type=mandel
  2. [ ] Derbyshire Nova, init: z=1; iterate: z=z-((z*z*z-1)/(3*z*z))+c;
  3. [X] Ushiki's Phoenix, z=z*z-.5*z+c; z=z*z-.5*z2+c; z2=z; z=z1; type=phoenix, mandphoenix, phoenixcplx, mandphoenixclx
  4. [ ] Talis, z=((z*z)/(1+z))+c;
  5. [ ] Newton variation, z=((z*z*z-z-1)/(3*z*z-1)-z)*c;
  6. [ ] z=z-((z*z*z)+(c-1)*z-c)/(3*(z*z)+c-1);
  7. [ ] Newton variation, z = (z-(((z*z*z)+(c*z)-z-c)/((3*z*z)+c-1)))+c;
  8. [ ] Nova variant, init: z=1; iterate: z=z-((z*z*z*z-z)/(4*z*z*z-1)+c;
  9. [ ] Nova variant, init: z=1; iterate: z=z-((z*z*z*z-z)/(4*z*z*z-z)+c;
  10. [ ] z=z*z*z+c;
  11. [ ] z=z*z*z*z+c;
  12. [ ] z=z*z*z*z*z+c;
  13. [ ] z=z*z*z*z*z*z+c;
  14. [ ] z1=z*z+c; z=z*z+c*z2; z2=z;
  15. [ ] Phoenix II, z1=z; z=z*z + real(c) + imag(c)*z2; z2=z1;
  16. [ ] Phoenix III, z1=z; z=z*z*z + real(c) + imag(c)*z2; z2=z1;
  17. [ ] Phoenix IV, z1=z; z=z*z*z +.5*real(c) + imag(c)*z2; z2=z1;
  18. [ ] z=-z/3; iterate: z=z-(z*z*z+z*z*c-z+c)/(3*z*z+2*c*z-1);
  19. [ ] z=-z/3; iterate: z=z-(z*z*z+z*z*c+z+c)/(3*z*z+2*c*z+1);
  20. [ ] z= z/2; iterate: z=z-(z^4-(z^3)*c-z-c)/(4*(z^3)-3*(z^2)*c-1)
  21. [ ] z=-1/(3*z); iterate: z=z-((z^3)*c+z^2+z+c)/(3*(z^2)*c+2*z+1)
  22. [ ] z=-.5; iterate: z=z-((z^4)c+(z^3)*c+z+c)/(4*(z^3)*c+3*z*z*c+1)
  23. [ ] z=-.5/z; iterate: z=z-((z^4)*c+(z^3)+z+c)/(4*(z^3)*c+3*z*z+1)
  24. [ ] z=-z/3; iterate: z=z-((z^3)+z*z*c +c)/(3*z*z+2*z*c)
  25. [ ] z=-z/2; iterate: z=z-((z^4)+(z^3)*c+c)/(4*(z^3)+3*z*z*c)
  26. [ ] 5th order Newton Mset
  27. [ ] 7th order Newton Mset
  28. [ ] 9th order Newton Mset
  29. [ ] 13th order Newton Mset
  30. [ ] 8th order Newton Mset
  31. [ ] Newton Diamond
  32. [ ] Newton Pentagon
  33. [ ] Newton Hexagon
  34. [ ] Newton Octagon
  35. [ ] 13th order Newton Flower
  36. [ ] z=z-(z*z*z*z*c-z+c)/(4*z*z*z*c);
  37. [ ] z=z-(z*z*z-z+c)/(3*z*z);
  38. [ ] z=z-(z*z*z*c-z*c-1)/(3*z*z*c);
  39. [ ] z=z-(z*z*z*c-z*z*c-1)/(3*z*z*c);
  40. [ ] z=z-(z*z*z*c-1)/(3*z*z*c);
  41. [ ] z=z-(z*z*z*c-z-1)/(3*z*z*c-z);
  42. [ ] z=z-(z*z*z*c-z*c-1)/(3*z*z*c-z);
  43. [ ] z=z-(z*z*z*c-z*z-1)/(3*z*z*c-3*z*z-3*z);
  44. [ ] z=z-(z*z*z*c-z*z*c-1)/(3*z*z*c-z*c-z);
  45. [ ] z=((z-(z*z*z-z)/(3*z*z-1))^2)*c;
  46. [ ] z = ccos(z*c)*c;
  47. [ ] z = ((((z*z).csin())*z/2)^2)+c, Sharon 14
  48. [ ] z = ((z*z).csin()).clog()+c;
  49. [ ] z = z*z*sin(z.real()) + c*z*cos(z.imag()) + c;
  50. [ ] z = csin(z)*ccos(c);
  51. [ ] z = csin(z*z*z*z)*c;
  52. [ ] 8th order Newton flower
  53. [ ] 6th order Newton Mset
  54. [ ] 15th order Newton Mset flower
  55. [ ] 4th order Newton's apple
  56. [ ] 25th order Newton Mset flower
  57. [ ] 38th order Newton Mset flower
  58. [ ] 50th order Newton Mset flower
  59. [ ] 5th order Newton Mset
  60. [ ] 18th order Newton Mset flower
  61. [ ] z=z*z+c; real=imag; imag=real
  62. [ ] z=(((z^3)-z-1)/((z^3)-1)-z)*c;
  63. [ ] z=(((z^4)-z*z-1)/(4*z*z-1)-z)*c;
  64. [ ] z=(z-((z^3)-1)/(3*z*z-fabs(z)-1))*c;
  65. [ ] z=(z-((z^3)-1)/(3*z*z-z-1))*c;
  66. [ ] z=(((z^4)-z-1)/(4*(z^3)-z-1)-z)*c;
  67. [ ] z=z-(((z^3)-z)/((3*z*z-1)))+c;
  68. [ ] z=(z-((z^3)-1)/(4*z*z-z-1))*c;
  69. [ ] z=(z-((z^3)-1)/(3*z*z-z))*c;
  70. [ ] z=(z-((z^4)-1)/(4*(z^3)-z))*c;
  71. [ ] z=(z-((z^4)-1)/(3*(z^3)-z))*c;
  72. [ ] z=(z-((z^4)-z-1)/(3*(z^3)-z))*c;
  73. [ ] z=c*(z-((z^3)-z)/(3*z*z-1));
  74. [ ] z=((1-z-(z^4))/(z-(4*(z^3)))-z)*c;
  75. [ ] z=((z-(z^3)*z)/(z-(3*(z^3)))-z)*c;
  76. [ ] z=((z-(z^3))/(z-(3*(z^3)))-z)*c;
  77. [ ] z=(((z^3)-1)/(2*z*z-1)-z)*c;
  78. [ ] z=(((z^3)-z-1)/(3*(z^3)-1)-z)*c;
  79. [ ] CBAP F(z) = Z^3 - 3*(A^2)*Z + B(MOD 2)
  80. [ ] z=.5; z=z*z-z2*z2+c; z2=z;
  81. [ ] z2=2; z=z*z*z*z+z2+c; z2=z1;
  82. [ ] z2=z; z=z*z*z*z+5*z2*c; z2=z1;
  83. [ ] t=0; z1=z; z=z*z*z-t*t*t+c; z=z1;
  84. [ ] t=0; z1=z; z=z*z*z*z-t*t*t*t+c; t=z1;
  85. [ ] z2=z; z=(z^4)+c; c=z2;
  86. [ ] z=z-((z^4)-z)/(4*(z^3)-1); z=z*z*c;
  87. [ ] z=z-((z^3)-1)/(3*z*z); z=(z^3)*c;
  88. [ ] z=z-((z^4)-1)/(4*(z^3)); z=(z^4)*c;
  89. [ ] z=z-((z^5)-1)/(5*(z^4)); z=(z^5)*c;
  90. [ ] z=z+c [quad]
  91. [ ] z=z*z*z-caa3*z+cb; [CCAP]
  92. [ ] z=z*z*z-caa3*z+cb; [CFAP]
  93. [ ] z1=z; z=z*z*z*z-z2+c; z2 = z1;
  94. [ ] z=c*z*(2 - z*z);
  95. [ ] z=z*z*z*z/t1+c;
  96. [ ] z1=z; z=z*z*z*z+z2/2+c;; z2=z1;
  97. [ ] z = z*z+c*(1+sqrt(z));
  98. [ ] z1=z; z=z*z*z*z/(1+z)+c;; c=z1;
  99. [ ] z1=z; z2=c+z2/z-z; z=z*c+z2/c;
  100. [ ] real(z) += sin(real(z)); z=z*z+c;
  101. [ ] z = ((z*z+c-1)/(2*z+c-2))^2; [magneto 1]
  102. [ ] z = ((z*z*z+3*c2*z+c1)/(3*z*z+3*c2*z+c1+1))^2; [magneto 2]
  103. [ ] z = ((z*z+c)/(2*z))^2;
  104. [ ] 3rd order Newton/ Mset [figure 8]
  105. [ ] 5th order N/Mset
  106. [ ] z1 = z; z = sin(z) - c; c = 1/(z*50); [quartet]
  107. [ ] z=(z*c)/(1+z)+c; [Talis II]
  108. [ ] z=(c+z*z*c)/(1-z*z*c);
  109. [ ] z = (c+(z^6))/(1+(z^2));
  110. [ ] z = (z^2)/(1+c*(z^2));
  111. [ ] z = c*cos(z);
  112. [ ] z = c*sin(z);
  113. [ ] z = c*exp(z);
  114. [ ] z=z^2+c; c=c/2+z [spider]
  115. [ ] z = (c/sin(z))^2;
  116. [ ] z = (c/cos(z))^2;